Methods for accurate sequence data and modified base position determination

ABSTRACT

Disclosed herein are methods of determining the sequence and/or positions of modified bases in a nucleic acid sample present in a circular molecule with a nucleic acid insert of known sequence comprising obtaining sequence data of at least two insert-sample units. In some embodiments, the methods comprise obtaining sequence data using circular pair-locked molecules. In some embodiments, the methods comprise calculating scores of sequences of the nucleic acid inserts by comparing the sequences to the known sequence of the nucleic acid insert, and accepting or rejecting repeats of the sequence of the nucleic acid sample according to the scores of one or both of the sequences of the inserts immediately upstream or downstream of the repeats of the sequence of the nucleic acid sample.

This is a divisional of U.S. patent application Ser. No. 13/492,593filed Jun., 8 2012, which is a divisional of U.S. patent applicationSer. No. 12/613,291, filed Nov. 5, 2009, and claims the benefit of U.S.Provisional Patent Application No. 61/112,548, filed on Nov. 7, 2008,and of U.S. Provisional Patent Application No. 61/167,313, filed on Apr.7, 2009, all of which are incorporated herein by reference.

The present invention relates to methods of determining the sequence ofnucleic acids and of identifying the positions of modified bases innucleic acids.

BACKGROUND OF THE INVENTION

Recent developments in DNA sequencing technology have raised thepossibility of highly personalized, preventive medicine on the genomiclevel. Additionally, the possibility of rapidly acquiring large amountsof sequence data from multiple individuals within one or morepopulations may usher in a new phase of the genomics revolution inbiomedical science.

Single base differences between genotypes can have substantialphenotypic effects. For example, over 300 mutations have been identifiedin the gene encoding phenylalanine hydroxylase (PAH), the enzyme thatconverts phenylalanine to tyrosine in phenylalanine catabolism andprotein and neurotransmitter biosynthesis that result in a deficientenzyme activity and lead to the disorders hyperphenylalaninaemia andphenylketonuria. See, e.g., Jennings et al., Eur J Hum Genet. 8, 683-696(2000).

Sequence data can be obtained using the Sanger sequencing method, inwhich labeled dideoxy chain terminator nucleotide analogs areincorporated in a bulk primer extension reaction and products ofdiffering lengths are resolved and analyzed to determine the identity ofthe incorporated terminator. See, e.g., Sanger et al., Proc Natl AcadSci USA 74, 5463-5467 (1997). Indeed, many genome sequences have beendetermined using this technology. However, the cost and speed ofacquiring sequence data by Sanger sequencing can be limiting.

New sequencing technologies can produce sequence data at an astoundingrate—hundreds of megabases per day, with costs per base lower than forSanger sequencing. See, e.g., Kato, Int J Clin Exp Med 2, 193-202(2009). However, the raw data obtained using these sequencingtechnologies can be more error prone than traditional Sanger sequencing.This can result from obtaining information from individual DNA moleculesinstead of a bulk population.

For example, in single molecule sequencing by synthesis, a base could beskipped due to the device missing a weak signal, or due to lack ofsignal resulting from fluorescent dye bleaching, or due to thepolymerase acting too fast to be detected by device. All of the aboveevents result in a deletion error in the raw sequence. Similarly,mutation errors and insertion errors can also happen at a higherfrequency for the simple reasons of potentially weaker signals andfaster reactions than in conventional methods.

Low accuracy sequence data is more difficult to assemble. In large scalesequencing, such as sequencing a complete eukaryotic genome, the DNAmolecules are fragmented into smaller pieces. These pieces are sequencedin parallel, and then the resultant reads are assembled to reconstructthe whole sequence of the original sample DNA molecules. Thefragmentation can be achieved, for example, by mechanical shearing orenzymatic cleavage.

Assembly of small reads of sequence into a large genome requires thatthe fragmented reads are accurate enough to be correctly groupedtogether. This is generally true for the raw sequencing data generatedfrom the Sanger method, which can have a raw data accuracy of higherthan 95%. Accurate single molecular sequencing technology could beapplied to detect single-base modifications or mutations nucleic acidsamples. However, the raw data accuracy for single molecule sequencingtechnologies may be lower due to the limitations discussed above. Theaccuracy of individual reads of raw sequence data could be as low as 60to 80%. See, e.g., Harris et al., Science 320:106-109 (2008). Thus, itwould be useful to provide accurate single molecule sequencing methods.

Additionally, DNA methylation plays a critical role in the regulation ofgene expression; for example, methylation at promoters often leads totranscriptional silencing. Methylation is also known to be an essentialmechanism in genomic imprinting and X-chromosome inactivation. However,progress in deciphering complex whole genome methylation profiles hasbeen limited. Therefore, methods of determining DNA methylation profilesin a high-throughput manner could be useful, more so should the methodsalso provide for accurate determination of sequence.

SUMMARY OF THE INVENTION

In some embodiments, the invention provides a method of determining thesequence of a nucleic acid sample comprising (a) providing a circularnucleic acid molecule comprising at least one insert-sample unitcomprising a nucleic acid insert and the nucleic acid sample, whereinthe insert has a known sequence; (b) obtaining sequence data comprisingsequence of at least two insert-sample units, wherein a nucleic acidmolecule is produced that comprises at least two insert-sample units;(c) calculating scores of the sequences of at least two inserts of thesequence data of step (b) by comparing the sequences to the knownsequence of the insert; (d) accepting or rejecting at least two of therepeats of the sequence of the nucleic acid sample of the sequence dataof step (b) according to the scores of one or both of the sequences ofthe inserts immediately upstream and downstream of the repeat of thesequence of the nucleic acid sample; (e) compiling an accepted sequenceset comprising at least one repeat of the sequence of the nucleic acidsample accepted in step d; and (f) determining the sequence of thenucleic acid sample using the accepted sequence set.

In some embodiments, the invention provides a system comprising asequencing apparatus operably linked to a computing apparatus comprisinga processor, storage, bus system, and at least one user interfaceelement, the storage being encoded with programming comprising anoperating system, user interface software, and instructions that, whenexecuted by the processor, optionally with user input, perform a methodcomprising: (a) obtaining sequence data from a circular nucleic acidmolecule comprising at least one insert-sample unit comprising a nucleicacid insert and a nucleic acid sample, wherein: (i) the insert has aknown sequence, (ii) the sequence data comprise sequence of at least twoinsert-sample units, and (iii) a nucleic acid molecule is produced thatcomprises at least two insert-sample units; (b) calculating scores ofthe sequences of at least two inserts of the sequence data of step (a)by comparing the sequences to the known sequence of the insert; (c)accepting or rejecting at least two of the repeats of the sequence ofthe nucleic acid sample of the sequence data of step (a) according tothe scores of one or both of the sequences of the inserts immediatelyupstream and downstream of the repeat of the sequence of the nucleicacid sample; (d) compiling an accepted sequence set comprising at leastone repeat of the sequence of the nucleic acid sample accepted in step(c); and (e) determining the sequence of the nucleic acid sample usingthe accepted sequence set, wherein an output of the system is used toproduce at least one of (i) a sequence of a nucleic acid sample or (ii)an indication that there is a modified base in at least one position ina nucleic acid sample.

In some embodiments, the invention provides a storage encoded withprogramming comprising an operating system, user interface software, andinstructions that, when executed by the processor on a system comprisinga sequencing apparatus operably linked to a computing apparatuscomprising a processor, storage, bus system, and at least one userinterface element, optionally with user input, perform a methodcomprising: (a) obtaining sequence data from a circular nucleic acidmolecule comprising at least one insert-sample unit comprising a nucleicacid insert and a nucleic acid sample, wherein: (i) the insert has aknown sequence, (ii) the sequence data comprise sequence of at least twoinsert-sample units, and (iii) a nucleic acid molecule is produced thatcomprises at least two insert-sample units; (b) calculating scores ofthe sequences of at least two inserts of the sequence data of step (a)by comparing the sequences to the known sequence of the insert; (c)accepting or rejecting at least two of the repeats of the sequence ofthe nucleic acid sample of the sequence data of step (a) according tothe scores of one or both of the sequences of the inserts immediatelyupstream and downstream of the repeat of the sequence of the nucleicacid sample; (d) compiling an accepted sequence set comprising at leastone repeat of the sequence of the nucleic acid sample accepted in step(c); and (e) determining the sequence of the nucleic acid sample usingthe accepted sequence set, wherein the method results in output used toproduce at least one of (i) a sequence of a nucleic acid sample or (ii)an indication that there is a modified base in at least one position ina nucleic acid sample.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample and a position of atleast one modified base in the sequence, comprising: (a) locking theforward and reverse strands together to form a circular pair-lockedmolecule; (b) obtaining sequence data of the circular pair-lockedmolecule via single molecule sequencing, wherein the sequence datacomprises sequences of the forward and reverse strands of the circularpair-locked molecule; (c) determining the sequence of thedouble-stranded nucleic acid sample by comparing the sequences of theforward and reverse strands of the circular pair-locked molecule; (d)altering the base-pairing specificity of bases of a specific type in thecircular pair-locked molecule to produce an altered circular pair-lockedmolecule; (e) obtaining the sequence data of the altered circularpair-locked molecule wherein the sequence data comprises sequences ofthe altered forward and reverse strands; and (f) determining thepositions of modified bases in the sequence of the double-strandednucleic acid sample by comparing the sequences of the altered forwardand reverse strands.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample, comprising: (a)locking the forward and reverse strands of the nucleic acid sampletogether to form a circular pair-locked molecule; (b) obtaining sequencedata of the circular pair-locked molecule via single moleculesequencing, wherein sequence data comprises sequences of the forward andreverse strands of the circular pair-locked molecule; and (c)determining the sequence of the double-stranded nucleic acid sample bycomparing the sequences of the forward and reverse strands of thecircular pair-locked molecule.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample and a position of atleast one modified base in the sequence, comprising: (a) locking theforward and reverse strands of the nucleic acid sample together to forma circular pair-locked molecule; (b) obtaining sequence data of thecircular pair-locked molecule via single molecule sequencing, whereinsequence data comprises sequences of the forward and reverse strands ofthe circular pair-locked molecule; and (c) determining the sequence ofthe double stranded nucleic acid sample and the position of the at leastone modified base in the sequence of the double stranded nucleic acidsample by comparing the sequences of the forward and reverse strands ofthe circular pair-locked molecule.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample and a position of atleast one modified base in the sequence, comprising: (a) locking theforward and reverse strands of the nucleic acid sample together to forma circular pair-locked molecule; (b) altering the base-pairingspecificity of bases of a specific type in the circular pair-lockedmolecule; (c) obtaining sequence data of the circular pair-lockedmolecule via single molecule sequencing, wherein sequence data comprisessequences of the forward and reverse strands of the circular pair-lockedmolecule; and (d) determining the sequence of the double-strandednucleic acid sample and the position of the at least one modified basein the sequence of the double-stranded nucleic acid sample by comparingthe sequences of the forward and reverse strands of the circularpair-locked molecule.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample and a position of atleast one modified base in the sequence, comprising: (a) locking theforward and reverse strands together to form a circular pair-lockedmolecule; (b) obtaining sequence data of the circular pair-lockedmolecule via single molecule sequencing, wherein the sequence datacomprises sequences of the forward and reverse strands of the circularpair-locked molecule; (c) determining the sequence of thedouble-stranded nucleic acid sample by comparing the sequences of theforward and reverse strands of the circular pair-locked molecule; (d)obtaining sequencing data of the circular pair-locked molecule viasingle molecule sequencing, wherein at least one nucleotide analog thatdiscriminates between a base and its modified form is used to obtainsequence data comprising at least one position wherein the at least onedifferentially labeled nucleotide analog was incorporated; and (e)determining the positions of modified bases in the sequence of thedouble-stranded nucleic acid sample by comparing the sequences of theforward and reverse strands.

In some embodiments, the invention provides a method of determining asequence of a double-stranded nucleic acid sample and a position of atleast one modified base in the sequence, comprising: (a) locking theforward and reverse strands of the nucleic acid sample together to forma circular pair-locked molecule; (b) obtaining sequence data of thecircular pair-locked molecule via single molecule sequencing, wherein atleast one nucleotide analog that discriminates between a base and itsmodified form is used to obtain sequence data comprising at least oneposition wherein the at least one differentially labeled nucleotideanalog was incorporated; and (c) determining the sequence of thedouble-stranded nucleic acid sample and the position of the at least onemodified base in the sequence of the double-stranded nucleic acid sampleby comparing the sequences of the forward and reverse strands of thecircular pair-locked molecule.

Additional objects and advantages of the invention will be set forth inpart in the description which follows, and in part will be obvious fromthe description, or may be learned by practice of the invention. Theobjects and advantages of the invention will be realized and attained bymeans of the elements and combinations particularly pointed out in theappended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments of theinvention and together with the description, serve to explain theprinciples of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and advantages of this invention may becomeapparent from the following detailed description with reference to theaccompanying drawings in which:

FIG. 1. Preparation of a circular DNA molecule in accordance with someembodiments of the invention. A DNA sample 1 is fragmented; a fragment 2is ligated at its 5′ end (diamond) to a linker 3 and at its 3′ end(arrowhead) to another linker 4. The linkers 3 and 4 are complementaryto adjoining segments of an oligonucleotide 5. Annealing of 5 to 3 and 4provides a substrate for circularization by ligation, which reactionresults in a circular molecule 6 comprising a nucleic acid insert (fromthe sequence of the linkers 3 and 4) and a nucleic acid sample (from thesequence of the fragment 2).

FIG. 2. Rolling circle amplification. An oligonucleotide 5, annealed toa circular molecule 6 produced as in FIG. 1, is bound by a polymerase 7anchored to a surface 8. Extension of the oligonucleotide gives acomplementary linear copy 9 of the circular molecule. Continuedextension results in strand displacement and synthesis of a molecule 10containing multiple copies of the circular molecule.

FIG. 3. Circular pair-locked molecule. (A) A double stranded moleculecontaining a forward strand 11 and reverse strand 12 can be combinedwith inserts that form hairpins 13 and 14, which may be identical ornon-identical, to form a circular pair locked molecule. In someembodiments, the linkers have overhangs and recessed ends (37 and 38).These can be filled in using a polymerase or may be complementary tooverhangs in the double stranded molecule (not shown). In a completecircular pair-locked molecule, 37 and 38 are filled in and sealed sothat the molecule has a continuous, single stranded, and circularbackbone. (B) After gap filling and end joining as appropriate, acircular DNA is formed containing the forward strand 11, linker 14,reverse strand 12, and linker 13, shown here in melted form. Themolecule can be converted to double stranded form, for example, byannealing a primer to one of the linkers and extending it using apolymerase without strand displacement activity, for example, E. coliDNA polymerase I, followed by ligation.

FIG. 4. Schemes for sequence determination and sequence and methylationprofile determination using circular pair-locked molecules. (Left) Acircular pair locked molecule can be sequenced for at least one fulllength of the molecule to provide complementary sequence reads;continued sequencing can be used to provide additional redundancy. Thesequence data can be aligned and evaluated based on the sequences of theinsert nucleic acids so as to obtain accurate sequence of the samplenucleic acid. (Right) Conversion of a specific type of nucleotide, suchas by bisulfite conversion or photochemical transition, followed bysequencing, alignment, and comparison of the modified sequence and itsunmodified complement can be used to obtain accurate sequence data andmethylation profiles. Extended sequence reads containing multiplerepeats of the sample nucleic acid sequence can be used for increasedaccuracy.

FIG. 5. Nucleotide conversion. (A) A circular pair-locked moleculecontaining inserts 13 and 14, a forward strand 15 containing at leastone 5-methylcytosine (^(m)C) residue, and a reverse strand 16 issubjected to treatment, such as photochemical transition, to convert^(m)C to T, resulting in converted forward strand 17. The complementarynucleotide in the reverse strand is unaffected, resulting in a G-Twobble pair. (^(m)C residues in the reverse strand, if present, would beconverted by the treatment.) (B) A circular pair-locked moleculecontaining inserts 13 and 14, a forward strand 15 containing at leastone 5-methylcytosine (^(m)C) residue, and a reverse strand 16 issubjected to treatment, such as bisulfite conversion, to convert C (butnot ^(m)C) to U, resulting in converted forward strand 39 and convertedreverse strand 40. The nucleotides complementary to the convertednucleotides are unaffected, resulting in G-U wobble pairs.

FIG. 6. Obtaining sequence data and a methylation profile from acircular pair-locked molecule. (A) A primer 18 is annealed to theconverted circular pair-locked molecule of FIG. 5A and extended by apolymerase, resulting in synthesis of a strand with segments 19, 20, and21, complementary to the sequences of 16, 14, and 17, respectively. (B)Sequence is obtained comprising at least two repeats: at least one of arepeat of the sample 17 and a repeat of the newly synthesized complementof the forward strand 21; and at least one of a repeat of the newlysynthesized complement of the reverse strand 19 and a repeat of thereverse strand 16. These repeats are aligned; a position 41 at whichthere is disagreement among the repeats signifies that a base wasmodified at that position. Depending on the type of modification used,the bases originally present at the corresponding position of thenucleic acid sample can be determined. In this example, where thecircular pair locked molecule has been modified by conversion of ^(m)Cto T (see FIG. 5A), the disagreement indicates that a ^(m)C was presentin the nucleic acid sample in the forward strand at position 41; thelogic is that at a position where the sequences disagree, the base whichis the product of the conversion reaction, T, has replaced the substrateof the conversion reaction, ^(m)C, which was present in the nucleic acidsample.

FIG. 7. Raw and processed sequence data acquired from a circular nucleicacid molecule template. (A) The content of sequence that can be obtainedfrom a circular template is represented diagrammatically. Nucleic acidsample sequence is represented by dashes and nucleic acid insertsequence is represented by circles. The sequence illustrated begins witha partial sequence 22 of a nucleic acid sample, followed by the sequenceof a nucleic acid insert 23; these are followed by a sequence 24 of thenucleic acid sample, a sequence 25 of a nucleic acid insert, a sequence26 of the nucleic acid sample, and a sequence 27 of a nucleic acidinsert. 28 represents additional sequence not shown in this figure,which is followed by a sequence 29 of a nucleic acid insert, a sequence30 of the nucleic acid sample, a sequence 31 of a nucleic acid insert,and a partial sequence 32 of a nucleic acid sample.

If the circular template comprises a single nucleic acid sample and asingle nucleic acid insert, then both of 22 and 24, along withsubsequent nucleic acid sample sequences 26, 30, and 32, are sequencesof the same single nucleic acid sample; likewise, 23, 25, 27, 29, and 31are sequences of the same single nucleic acid insert in this case. Ifthe circular template comprises forward and reverse repeats of thesequence of the nucleic acid sample and two nucleic acid inserts havingknown sequences, which may be identical or non-identical, as in the caseof a circular pair-locked molecule, then the nucleic acid samplesequences have alternating orientations and correspond to the twonucleic acid sample repeats in an alternating manner (e.g., 22 could bein forward orientation, meaning it is a sequence of the reverse repeat,and 24 could be in reverse orientation, meaning it is a sequence of theforward repeat, or vice versa). Likewise, the nucleic acid insertsequences 23, 25, etc., would also correspond to the two nucleic acidinserts, which may be identical or non-identical, of the circulartemplate in an alternating manner.

(B) The sequence shown in FIG. 7A can be decomposed into segments eachcontaining a repeat of the nucleic acid sample sequence, e.g., 24; thesegments also comprise at least one repeat of the nucleic acid insert,for example, two repeats of the nucleic acid insert, e.g., 23 and 25.Some segments may contain only a partial sequence, e.g., 33, or anunusually long sequence, e.g., 34. Such segments can result from errorsduring sequencing. In some embodiments, such segments are excluded fromfurther consideration.

FIG. 8. Diagram of sequence processing steps. In some embodiments, rawsequence data are examined, processed, and accepted or rejected asshown. A raw sequence database 35 may be used. If a score is calculatedthat exceeds a threshold, a step 36 may be performed: accept the samplesequence and add it to an accepted sequence set.

FIG. 9. Rolling circle amplification products. Products of the reactionsdescribed in Example 1 were electrophoresed and the gel was visualizedas described. From the left, C1 and C2 are negative control lanes. Theleftmost Mr lane contains the FERMENTAS GENERULER 1 kb ladder, Cat. No.SM0311, which band sizes ranging from 250 to 10,000 bp. The next tenlanes contain products of rolling circle amplification reactions asindicated, generated using two primers or one primer (amplificationcontrol) and products of the L0 (negative ligation control) or L3reactions ligation reactions taken at the indicated times; seeExample 1. The next Mr lane contains the FERMENTAS GENERULER 100 bp Plusladder, Cat. No. SM0321, with band sizes ranging from 100 to 3,000 bp.The next ten lanes contain the same products as in the previous tenproduct lanes except that these products were mixed with loading dyecontaining 1% SDS.

FIG. 10. Alignments showing repeat sequences and deduced originalsequence of a simulated nucleic acid sample. Positions where all alignedsequences agree are marked by asterisks. (A) Reads a (residues 1 to 35of SEQ ID NO: 10) and b (residues 1 to 35 of SEQ ID NO: 11) of Example 2are shown together with the deduced original sequence, labeled ‘o’ (SEQID NO: 5), of the forward strand of the nucleic acid sample. Theoriginal sequence was deduced using the rules shown in Table 5. Thepositions where all three sequences shown have C are positions where thesimulated nucleic acid sample contained a methylated cytosine in theforward strand. The positions where all three sequences shown have G arepositions where the simulated nucleic acid sample contained a methylatedcytosine in the reverse strand. (B) Reads a (SEQ ID NO: 14) and b (SEQID NO: 15) of Example 3 are shown together with the deduced originalsequence of the forward strand, marked ‘r_a’ (SEQ ID NO: 5). Theoriginal sequence was deduced using the rules in Table 6. The positionswhere the deduced original sequence has a C that disagrees with read aare positions where the simulated nucleic acid sample contained amethylated cytosine in the forward strand. The positions where thededuced original sequence has a G that disagrees with read b arepositions where the simulated nucleic acid sample contained a methylatedcytosine in the reverse strand.

FIG. 11. Computing apparatus and storage. (A) In some embodiments, theinvention relates to a sequencing apparatus 51 operably linked to acomputing apparatus 52 comprising at least one user interface elementchosen from a display 57, a keyboard 58, and a mouse 59, and at leastone computer 53 comprising a storage 54 (see panel B), a bus system 55,and a processor 56. (B) In some embodiments, the invention relates to astorage 54 comprising an operating system 60, user interface software61, and processing software 62. The storage can additionally comprisesequence data 63 acquired from the sequencing apparatus (51 in FIG.11A).

FIG. 12. General scheme of sequence and 5-methylcytosine positiondetermination of using bisulfite conversion with a linear pair lockedmolecule. A double stranded nucleic acid sample comprising5-methylcytosine is provided (at top). A linear pair-locked molecule isconstructed by ligating a hairpin insert to one double strand end of themolecule (beneath first arrow, at right), thereby locking the forwardand reverse strands of the double-stranded sample together. Also, linearflaps are attached to the other double strand end (at left). Bisulfiteconversion is performed, converting cytosines to uracils but leaving5-methylcytosines unaffected. The molecule is copied by providing aprimer that binds to the linear flap attached at the 3′ end of thelinear pair locked molecule and extending the primer with a polymerase.The ends can be processed, e.g., by restriction digestion, to preparethe molecule for subsequent cloning and/or sequencing.

FIG. 13. General scheme of sequence and 5-methylcytosine positiondetermination using photochemical transition with a linear pair lockedmolecule. A double stranded nucleic acid sample comprising5-methylcytosine is provided (at top). A linear pair-locked molecule isconstructed by ligating a hairpin insert to one double strand end of themolecule (beneath first arrow, at right), thereby locking the forwardand reverse strands of the double-stranded sample together. Also, linearflaps are attached to the other double strand end (at left).Photochemical transition is performed, converting 5-methylcytosines tothymines but leaving unmodified cytosines unaffected. The molecule iscopied by providing a primer that binds to the linear flap attached atthe 3′ end of the linear pair locked molecule and extending the primerwith a polymerase. The ends can be processed, e.g., by restrictiondigestion, to prepare the molecule for subsequent cloning and/orsequencing.

FIG. 14. General scheme of sequence determination using a circular pairlocked molecule. A double stranded nucleic acid sample is provided (attop) (top strand: SEQ ID NO: 5; bottom strand: SEQ ID NO: 6). A circularpair-locked molecule is constructed by ligating a hairpin insert to bothdouble strand ends of the molecule (beneath first arrow, at right andleft), thereby locking the forward and reverse strands of thedouble-stranded sample together. Sequencing is performed, resulting inreads of SEQ ID NOs: 5 and 6, and the sequence data is analyzed todetermine the sequence of the sample (SEQ ID NOs: 5 and 6); see, e.g.,Example 5.

FIG. 15. General scheme of sequence and 5-methylcytosine positiondetermination using bisulfite conversion and a circular pair lockedmolecule. A double stranded nucleic acid sample comprising5-methylcytosine is provided (at top) (top strand: SEQ ID NO: 5; bottomstrand: SEQ ID NO: 6). A circular pair-locked molecule is constructed byligating a hairpin insert to both double strand ends of the molecule(beneath first arrow, at right and left), thereby locking the forwardand reverse strands of the double-stranded sample together. Bisulfiteconversion is performed, converting cytosines to uracils but leaving5-methylcytosines unaffected. The product contains residues 1-35 and40-74 of SEQ ID NO: 8. Sequencing is performed, resulting in reads ofresidues 1-35 and 40-74 of SEQ ID NO: 9, and the sequence data isanalyzed to determine the sequence of the sample and 5-methylcytosinepositions (SEQ ID NOs: 5 and 6); see, e.g., Example 6.

FIG. 16. General scheme of sequence and 5-methylcytosine positiondetermination using photochemical transition and a circular pair lockedmolecule. A double stranded nucleic acid sample comprising5-methylcytosine is provided (at top) (top strand: SEQ ID NO: 5; bottomstrand: SEQ ID NO: 6). A circular pair-locked molecule is constructed byligating a hairpin insert to both double strand ends of the molecule(beneath first arrow, at right and left), thereby locking the forwardand reverse strands of the double-stranded sample together.Photochemical transition is performed, converting 5-methylcytosines tothymines but leaving unmodified cytosines unaffected. The productcontains residues 1-35 and 40-74 of SEQ ID NO: 12. Sequencing isperformed, resulting in reads of residues 1-35 and 40-74 of SEQ ID NO:13, and the sequence data is analyzed to determine the sequence of thesample and 5-methylcytosine positions (SEQ ID NOs: 5 and 6); see, e.g.,Example 7.

FIG. 17. General scheme of sequence and 5-bromouracil positiondetermination using a circular pair locked molecule. A double strandednucleic acid sample comprising 5-bromouracil is provided (at top) (topstrand: SEQ ID NO: 16; bottom strand: SEQ ID NO: 17). A circularpair-locked molecule is constructed by ligating a hairpin insert to bothdouble strand ends of the molecule (beneath first arrow, at right andleft), thereby locking the forward and reverse strands of thedouble-stranded sample together. Sequencing is performed (resulting inreads of SEQ ID NOs: 18 and 19) and the sequence data is analyzed todetermine the sequence of the sample and 5-bromouracil positions (SEQ IDNOs: 16 and 17); see, e.g., Example 8.

DETAILED DESCRIPTION OF THE INVENTION Definitions

To facilitate the understanding of this invention, a number of terms aredefined below. Terms not defined herein have meanings as commonlyunderstood by a person of ordinary skill in the areas relevant to thepresent invention. Terms such as “a”, “an” and “the” are not intended torefer to only a singular entity, but include the general class of whicha specific example may be used for illustration. The terminology hereinis used to describe specific embodiments of the invention, but theirusage does not delimit the invention, except as outlined in the claims.

The term nucleic acid includes oligonucleotides and polynucleotides.

High stringency conditions for hybridization refer to conditions underwhich two nucleic acids must possess a high degree of homology to eachother to hybridize. Examples of high stringency conditions forhybridization include hybridization in 4× sodium chloride/sodium citrate(SSC), at 65 or 70° C., or hybridization in 4×SSC plus 50% formamide atabout 42 or 50° C., followed by at least one, at least two, or at leastthree washes in 1×SSC, at 65 or 70° C.

Melting temperature refers to the temperature at which half of a nucleicacid in solution exists in a melted state and half exists in an unmeltedstate, assuming the presence of sufficient complementary nucleic acid.In the case of an oligonucleotide present in excess over complementarysequence, melting temperature is the temperature at which half of thecomplementary sequence is annealed with the oligonucleotide. In the caseof a nucleic acid insert capable of forming a hairpin, meltingtemperature is the temperature at which half of the insert is in apartially self-hybridized “hairpin” form. As melting temperature iscondition dependent, melting temperatures of oligonucleotides discussedherein refer to the melting temperature in an aqueous solution of 50 mMsodium chloride, with the oligonucleotide at 0.5 μM. Meltingtemperatures can be estimated by various methods known in the art, forexample, using the nearest-neighbor thermodynamic parameters found inAllawi et al., Biochemistry, 36, 10581-10594 (1997) together withstandard thermodynamic equations.

A site in a nucleic acid molecule is suitable for primer binding if ithas a unique sequence in the nucleic acid molecule and is of a lengthand composition such that the complementary oligonucleotide has anacceptable melting temperature, for example, a melting temperatureranging from 45° C. to 70° C., from 50° C. to 70° C., from 45° C. to 65°C., from 50° C. to 65° C., from 55° C. to 70° C., from 60° C. to 70° C.,from 55° C. to 60° C., from 60° C. to 65° C., or from 50° C. to 55° C.

Extending a primer, oligonucleotide, or nucleic acid refers to adding atleast one nucleotide to the primer, oligonucleotide, or nucleic acid.This includes reactions catalyzed by polymerase or ligase activity.

A sequencing primer is an oligonucleotide that can bind to a site in anucleic acid molecule that is suitable for primer binding and beextended in a sequencing reaction so as to produce sequence data.

A nucleic acid insert is capable of forming a hairpin if it canpartially self-hybridize, and the self-hybridized form has a meltingtemperature of at least 15° C.

An overhang is a single stranded segment at the end of a double strandednucleic acid molecule or hairpin.

A repeat or repeat sequence is a sequence that occurs more than once ina nucleic acid. When repeats are present in a nucleic acid molecule, allinstances of the sequence, including the first instance, are consideredrepeats. Repeats include sequences that are reverse complements of eachother, such as occur in a circular pair-locked molecule. Repeats alsoinclude sequences that are not exactly identical but are derived fromthe same sequence, e.g., sequences that differ due to misincorporationevents or other polymerase errors during synthesis, or sequences thatwere initially identical or perfect reverse complements but differ dueto modification by a procedure such as photochemical transition orbisulfite treatment.

A nucleic acid insert and a nucleic acid sample are immediately upstreamor downstream of one another if there are no other intervening repeatsof the insert or sample between the insert and sample. In a singlestranded molecule, upstream refers to the 5′ direction and downstreamrefers to the 3′ direction. In a double stranded molecule, the polaritycan be determined arbitrarily or it can be determined according to thepolarity of directional elements such as promoters, coding sequences,etc., if a majority of such elements is oriented in the same way. Thepolarity of a promoter is that the direction of an initiating RNApolymerase's synthesis is downstream. The polarity of a coding sequenceis that the direction from start to stop codon is downstream.

Two repeats are in forward and reverse orientations relative to eachother, and have opposite orientations, if they are reverse complementsof each other or one or both are derivatives of the reverse complementof each other. Which repeat is considered forward can be arbitrary orcan be determined according to polarity of elements in the repeat, asdiscussed in the preceding paragraph.

A modified base is a base other than adenine, thymine, guanine,cytosine, or uracil that can be included in place of one or more of theaforementioned bases in a nucleic acid or nucleotide.

Ambiguity codes are codes that represent a combination of bases at asequence, in the sense that any of the represented bases could bepresent, for example: Y=pyrimidine (C, U, or T); R=purine (A or G);W=weak (A, T, or U); S=strong (G or C); K=keto (T, U, or G); M=amino (Cor A); D=not C (A, G, T, or U); V=not T or U (A, C, or G); H=not G (A,C, T, or U); B=not A (C, G, T, or U).

A position weight matrix is a matrix in which the rows correspond topositions in a nucleic acid sequence and the columns correspond tobases, or vice versa, and each element in the matrix is a weight for aparticular base at a particular position. A sequence can be scoredagainst a position weight matrix by summing the weights corresponding toeach base of the sequence; for example, if the sequence is ACG, thescore would be the sum of the weight for A in the first column of thematrix, the weight for C in the second column, and the weight for G inthe third column, assuming columns corresponded to positions. A positionweight matrix can be run over a sequence with a length greater than thenumber of positions in the matrix by iteratively scoring the sequenceagainst the matrix, in which the starting position is incremented by oneposition in each run. In this way, a position in the sequence thatproduces a maximum or minimum score against the matrix can beidentified.

Storage refers to a repository of digital information accessible by acomputer. It includes RAM, ROM, hard drives, non-volatile solid statememory, optical disks, magnetic disks, and equivalents thereof.

A data structure is an object or variable in a storage that containsdata. A data structure can contain scalar data (e.g., an individualcharacter, number, or string), an assembly of scalar data (e.g., amatrix or array of scalars), or a recursive assembly (e.g., a list,which can be multidimensional, comprising sub-lists, matrices, arrays,and/or scalars as elements, with the sub-lists able themselves tocontain sub-lists, matrices, arrays, and/or scalars as elements).

Nucleic Acid Sample

The methods of the invention comprise determining the sequence of anucleic acid sample and/or determining the positions of modified basesin a nucleic acid sample. The term “nucleic acid sample” refers to thenucleic acid whose sequence and/or modified base positions are to bedetermined in the methods of the invention.

The nucleic acid sample can be obtained from a sources including,without limitation, DNA (including without limitation genomic DNA, cDNA,mtDNA, chloroplast DNA, and extrachromosomal or extracellular DNA) orRNA (including without limitation mRNA, primary transcript RNA, tRNA,rRNA, miRNA, siRNA, and snoRNA). The nucleic acid sample can be from anindividual, patient, specimen, cell culture, biofilm, organ, tissue,cell, spore, animal, plant, fungus, protist, bacterium, archaeon, virus,or virion. In some embodiments, the nucleic acid sample is obtained asan environmental sample, e.g., from soil or a body of water; the nucleicacid sample may be obtained as an environmental sample without specificknowledge of whether the nucleic acid is of cellular, extracellular, orviral origin. In addition, the nucleic acid can be obtained from achemical or enzymatic reaction, including reactions in which synthetic,recombinant, or naturally occurring nucleic acid is modified by anenzyme, for example, a methyltransferase.

In some embodiments, the nucleic acid sample is a processed sample froma source such as one of those listed above. For example, the isolatednucleic acid can be fragmented by shearing, such as by sonication orpipetting through a narrow aperture, or enzymatic digestion, such aswith an endonuclease, which can be a restriction endonuclease. In someembodiments, the nucleic acid sample has at least one overhang. Theisolated nucleic acid may first be cloned and propagated in a host celland/or vector, e.g., as a bacterial or yeast artificial chromosome, aminichromosome, plasmid, cosmid, extrachromosomal element, orchromosomally integrated construct.

Providing a Circular Nucleic Acid Molecule

In some embodiments, the methods of the invention comprise providing acircular nucleic acid molecule comprising an insert-sample unitcomprising a nucleic acid insert and the nucleic acid sample, whereinthe insert has a known sequence. The circular nucleic acid molecule canbe single or double stranded.

In some embodiments, the circular nucleic acid molecule is provided byisolating it in circular form from its source, if part of its sequenceis known and thus can serve as the nucleic acid insert (e.g., aconserved motif within the sequence of a gene contained in the circularmolecule may be known, or the molecule may be known to contain asequence based on its ability to hybridize under high stringencyconditions to another nucleic acid of known sequence). In someembodiments, the sequence of the nucleic acid insert is known onlyinexactly, as would be the case when knowledge of the sequence isderived from stringent hybridization properties. In some embodiments,the sequence of the nucleic acid insert is known exactly, such as wouldbe the case when the circular nucleic acid molecule has a known backbonesequence or has been engineered to contain a known sequence.

In some embodiments, the circular nucleic acid molecule is provided byperforming an in vitro reaction or reactions to incorporate the nucleicacid sample into the circular molecule along with a nucleic acid insert.The in vitro reaction or reactions can in some embodiments compriseligation by a ligase and/or other strand joining reactions such as canbe catalyzed by various enzymes, including recombinases andtopoisomerases. DNA ligase or RNA ligase may be used to enzymaticallyjoin the two ends of a linear template, with or without an adaptermolecule or linkers, to form a circle. For example, T4 RNA ligasecouples single-stranded DNA or RNA, as described in Tessier et al., AnalBiochem, 158: 171-78 (1986). CIRCLIGASE™ (Epicentre, Madison, Wis.) mayalso be used to catalyze the ligation of a single stranded nucleic acid.Alternatively, a double stranded ligase, such as E. coli or T4 DNAligase, may be used to perform the circularization reaction.

In some embodiments, providing the circular nucleic acid moleculecomprises amplifying a nucleic acid template with primers (which may berandom primers with 5′ flaps of known sequence that can serve as thenucleic acid insert) comprising complementary regions and circularizingthe amplified nucleic acid, such as may be catalyzed by a ligase or arecombinase; the amplified nucleic acid may in some embodiments beprocessed at its ends, e.g., by restriction or phosphorylation, prior tocircularization.

In some embodiments, the circular nucleic acid molecule is provided byperforming chemical circularization. Chemical methods employ knowncoupling agents such as BrCN plus imidazole and a divalent metal,N-cyanoimidazole with ZnCl₂, 1-(3-dimethylaminopropyl)-3ethylcarbodiimide HCl, and other carbodiimides and carbonyldiimidazoles. The ends of a linear template may also be joined bycondensing a 5′-phosphate and a 3′-hydroxyl, or a 5′-hydroxyl and a3′-phosphate.

In some embodiments, the circular nucleic acid molecule is a circularpair-locked molecule (cPLM). This type of molecule is discussed indetail below.

Providing Forward and Reverse Repeats of the Nucleic Acid Sample;Circular Pair-Locked Molecules

In some embodiments, the methods of the invention comprise providingforward and reverse repeats of a nucleic acid sample and locking theforward and reverse strands together to form a cPLM. The generalstructure of a cPLM is shown in FIG. 3A. A cPLM is a single-strandedcircular nucleic acid molecule that comprises forward and reverserepeats of a nucleic acid sample; the repeats are bracketed by nucleicacid inserts, as shown in FIG. 3A. The nucleic acid inserts can beidentical or non-identical. In some embodiments, the inserts have alength of at least 50 nt or at least 100 nt. In some embodiments, theinserts have a length ranging from 50 or 100 nt to 10,000 or 50,000 nt.

The strands of a linear double stranded nucleic acid sample can belocked together to form a cPLM, for example, by ligating nucleic acidinserts that form hairpins to each end of the molecule. In someembodiments, the nucleic acid inserts that form hairpins have meltingtemperatures of at least 20° C., 25° C., 30° C., 35° C., 40° C., 45° C.,50° C., 55° C., 60° C., 65° C., or 70° C. The ligation can be blunt-endor sticky-end ligation. Hairpin structures have base-paired stem regionsand unpaired loop regions. In some embodiments, the insert nucleic acidcomprises a loop region of a size of at least 20, 22, 25, 30, or 35nucleotides. In some embodiments, this loop region is suitable forprimer binding. In some embodiments, the loop region binds a primer witha melting temperature of at least 45° C., 50° C., 55° C., 60° C., 65°C., or 70° C.

In some embodiments, the nucleic acid sample comprises different stickyends, such as could be generated by digestion using restriction enzymeswith different restriction sites, and these different sticky ends favorligation of different nucleic acid inserts. In some embodiments, thedouble stranded nucleic acid to be converted in this way can be obtainedby extending a random primer comprising a 5′ flap of known sequencealong a template comprising the desired sample sequence.

The strands of a double stranded nucleic acid can also be lockedtogether to form a cPLM by treatment with an enzyme that convertsdouble-strand ends to hairpins, for example, recombinases that form aphosphotyrosine linkage with one strand of a double stranded moleculefollowed by hairpin formation through nucleophilic attack on thephosphotyrosine linkage by the other strand. Members of the family, suchas λ integrase and Flp recombinase, are examples of such recombinases.See, e.g., Chen et al., Cell 69, 647-658 (1992); Roth et al., Proc NatlAcad Sci USA 90, 10788-10792 (1993). In some embodiments, the nucleicacid sample comprises recognition sequences for the enzyme that convertsdouble-strand ends to hairpins. In some embodiments, recognitionsequences for the enzyme that converts double-strand ends to hairpinsare attached to the nucleic acid sample, e.g., by ligation.

In some embodiments, the sample nucleic acid is initially obtained insingle stranded form and is converted to double stranded form prior toformation of a cPLM. This can be accomplished, for example, by ligatinga hairpin with an overhang to the 3′ end of the sample nucleic acid, andthen extending from the 3′ end of the ligated hairpin to synthesize acomplementary strand. A second hairpin can then be joined to themolecule to form a cPLM.

Nucleic Acid Insert

The methods of the invention comprise providing and/or using circularnucleic acid molecules, including cPLMs, comprising at least one nucleicacid insert. In some embodiments, the at least one nucleic acid inserthas a partially, inexactly, or completely known sequence, as discussedabove. In some embodiments, the sequence of the at least one nucleicacid insert is completely known. In some embodiments, the at least onenucleic acid insert comprises a suitable binding site for anoligonucleotide, including a sequencing primer. In some embodiments, theat least one insert nucleic acid forms a hairpin.

In some embodiments, the at least one nucleic acid insert has a lengthranging from 10 to 300, 15 to 250, 30 to 200, or 30 to 100 nucleotideresidues. In some embodiments, the at least one nucleic acid insert hasa melting temperature ranging from 45° C. to 70° C. or from 50° C. to65° C.

In some embodiments, the at least one nucleic acid insert comprises apromoter, for example, the T7 RNA polymerase promoter. See, e.g., Guo etal., J Biol Chem 280, 14956-14961 (2005). A promoter is recognized by anRNA polymerase as a site for initiating RNA synthesis. Additionalpromoters are also known in the art.

Insert-Sample Unit

The circular nucleic acid molecules used in the methods of the inventioncomprise at least one nucleic acid sample and at least one nucleic acidinsert grouped as at least one insert-sample unit. An insert-sample unitis a segment of nucleic acid in which a nucleic acid insert isimmediately upstream or downstream of a nucleic acid sample.

In some embodiments, the circular nucleic acid molecule is a cPLM, whichcomprises two insert-sample units; the nucleic acid samples in these twounits are in opposite orientations to each other, that is, one is aforward repeat of the nucleic acid sample and the other is a reverserepeat. It should be noted that the cPLM may be considered to comprisetwo insert-sample units wherein the inserts are either upstream ordownstream of the samples; that is, a cPLM conforming to the structureshown in FIG. 3B contains, in order, elements 11 (forward repeat), 14(insert), 12 (reverse repeat), and 13 (insert), with 13 connecting backto 11 to close the circle. No matter whether the insert-sample units areconsidered to be 11 with 14, and 12 with 13, or 13 with 11, and 14 with12, the molecule contains two insert-sample units. In embodiments inwhich the orientation of the insert and/or its positioning relative tothe sample is functionally significant, e.g., the insert comprises apromoter or a primer binding site, it may be most efficient to group theinsert-sample units so as to group the insert with the sample towardwhich the primer binding site or promoter is oriented, i.e., the samplewhich would be copied first by a polymerase initiating from the primerbinding site or promoter.

Obtaining Sequence Data

Sequencing Method

The methods of the invention comprise obtaining sequence data. In someembodiments, a nucleic acid molecule is produced that comprises at leasttwo insert sample units during the step of obtaining sequence data. Insome embodiments, the nucleic acid molecule comprising at least twoinsert sample units can be produced by synthesizing it from the providedcircular nucleic acid molecule. In some embodiments, the nucleic acidmolecule comprising at least two insert sample units can be produced byaltering the provided circular nucleic acid molecule, e.g., byconverting the circular nucleic acid molecule to a linear nucleic acidmolecule, which may be single-stranded in some embodiments. In someembodiments, at least one phosphodiester bond in a nucleic acidmolecule, which may be the provided circular nucleic acid molecule or atemplate synthesis product thereof, is formed or broken in the step ofobtaining sequence data.

In some embodiments, sequence data is obtained using a sequencing bysynthesis method. In some embodiments, sequence data is obtained using asingle molecule sequencing method. In some embodiments, the singlemolecule sequencing method is chosen from pyrosequencing, reversibleterminator sequencing, ligation sequencing, nanopore sequencing, andthird-generation sequencing.

In some embodiments, sequence data is obtained using a bulk sequencingmethod, for example, Sanger sequencing or Maxam-Gilbert sequencing.

Single molecule sequencing methods are distinguished from bulksequencing methods according to whether a single nucleic acid moleculeis isolated as part of the sequencing procedure. The nucleic acidmolecule may be single- or double-stranded; two annealed nucleic acidstrands are considered a single molecule for this purpose. The isolationof the single molecule may occur in a microwell, via use of a nanopore,by direct or indirect attachment in an optically resolvable manner to asubstrate such as a microscope slide, or in any other way that allowssequence data to be obtained from the individual molecule. In indirectattachment, the single molecule is attached to the substrate via alinking structure that binds to the single molecule, for example, aprotein or oligonucleotide. Notably, methods in which a single moleculeis isolated, then amplified, and sequence data is obtained directly fromthe amplification product(s) are still considered single moleculemethods because a single molecule was isolated and served as theultimate source of the sequence data. (In contrast, in bulk sequencingmethods, a nucleic acid sample is used that contains multiple moleculesand data is obtained containing signal that originated from multiplemolecules.) In some embodiments, single molecule sequencing is performedwherein redundant sequence is obtained from the same molecule. Theredundant sequence can be obtained by sequencing at least two direct orinverted repeats within a molecule, or by sequencing the same segment ofthe molecule more than once. The redundant sequence can be completelyredundant or partially redundant with some variation, e.g., due todifferences introduced by alteration of base pairing specificity ofbases of a certain type, or due to errors that may occur during thesequencing process. In some embodiments, the alteration of base pairingspecificity can occur prior to sequencing. In some embodiments, the samemolecule is sequenced multiple times, optionally with an interveningtreatment that selectively alters base pairing specificity of bases of acertain type occurring between the iterations of sequencing.

Sanger sequencing, which involves using labeled dideoxy chainterminators, is well known in the art; see, e.g., Sanger et al., ProcNatl Acad Sci USA 74, 5463-5467 (1997). Maxam-Gilbert sequencing, whichinvolves performing multiple partial chemical degradation reactions onfractions of the nucleic acid sample followed by detection and analysisof the fragments to infer the sequence, is also well known in the art;see, e.g., Maxam et al., Proc Natl Acad Sci USA 74, 560-564 (1977).Another bulk sequencing method is sequencing by hybridization, in whichthe sequence of a sample is deduced based on its hybridizationproperties to a plurality of sequences, e.g., on a microarray or genechip; see, e.g., Drmanac, et al., Nat Biotechnol 16, 54-58 (1998).

Single molecule sequencing methods are discussed generally, for example,in Kato, Int J Gun Exp Med 2, 193-202 (2009) and references therein.

Pyrosequencing, reversible terminator sequencing, and ligationsequencing are considered to be second-generation sequencing methods.Generally, these methods use amplification products generated from asingle molecule, which are spatially segregated from amplificationproducts generated from other molecules. The spatial segregation can beimplemented by using an emulsion, a picoliter well, or by attachment toa glass slide. Sequence information is obtained via fluorescence uponincorporation of a nucleotide; after acquiring data, the fluorescence ofthe newly incorporated nucleotide is eliminated and the process isrepeated for the next nucleotide.

In pyrosequencing, the pyrophosphate ion released by the polymerizationreaction is reacted with adenosine 5′ phosphosulfate by ATP sulfurylaseto produce ATP; the ATP then drives the conversion of luciferin tooxyluciferin plus light by luciferase. As the fluorescence is transient,no separate step to eliminate fluorescence is necessary in this method.One type of deoxyribonucleotide triphosphate (dNTP) is added at a time,and sequence information is discerned according to which dNTP generatessignificant signal at a reaction site. The commercially available RocheGS FLX instrument acquires sequence using this method. This techniqueand applications thereof are discussed in detail, for example, inRonaghi et al., Anal Biochem 242, 84-89 (1996) and Margulies et al.,Nature 437, 376-380 (2005) (corrigendum at Nature 441, 120 (2006)).

In reversible terminator sequencing, a fluorescent dye-labelednucleotide analog that is a reversible chain terminator due to thepresence of a blocking group is incorporated in a single-base extensionreaction. The identity of the base is determined according to thefluorophore; in other words, each base is paired with a differentfluorophore. After fluorescence/sequence data is acquired, thefluorophore and the blocking group are chemically removed, and the cycleis repeated to acquire the next base of sequence information. TheIllumina GA instrument operates by this method. This technique andapplications thereof are discussed in detail, for example, in Ruparel etal., Proc Natl Acad Sci USA 102, 5932-5937 (2005), and Harris et al.,Science 320, 106-109 (2008).

In ligation sequencing, a ligase enzyme is used to join a partiallydouble-stranded oligonucleotide with an overhang to the nucleic acidbeing sequenced, which has an overhang; in order for ligation to occur,the overhangs must be complementary. The bases in the overhang of thepartially double-stranded oligonucleotide can be identified according toa fluorophore conjugated to the partially double-strandedoligonucleotide and/or to a secondary oligonucleotide that hybridizes toanother part of the partially double-stranded oligonucleotide. Afteracquisition of fluorescence data, the ligated complex is cleavedupstream of the ligation site, such as by a type IIs restriction enzyme,for example, Bbvl, which cuts at a site a fixed distance from itsrecognition site (which was included in the partially double strandedoligonucleotide). This cleavage reaction exposes a new overhang justupstream of the previous overhang, and the process is repeated. Thistechnique and applications thereof are discussed in detail, for example,in Brenner et al., Nat Biotechnol 18, 630-634 (2000). In someembodiments, ligation sequencing is adapted to the methods of theinvention by obtaining a rolling circle amplification product of acircular nucleic acid molecule, and using the rolling circleamplification product as the template for ligation sequencing.

In nanopore sequencing, a single stranded nucleic acid molecule isthreaded through a pore, e.g., using an electrophoretic driving force,and sequence is deduced by analyzing data obtained as the singlestranded nucleic acid molecule passes through the pore. The data can beion current data, wherein each base alters the current, e.g., bypartially blocking the current passing through the pore to a different,distinguishable degree.

In third-generation sequencing, a slide with an aluminum coating withmany small (−50 nm) holes is used as a zero mode waveguide (see, e.g.,Levene et al., Science 299, 682-686 (2003)). The aluminum surface isprotected from attachment of DNA polymerase by polyphosphonatechemistry, e.g., polyvinylphosphonate chemistry (see, e.g., Korlach etal., Proc Natl Acad Sci USA 105, 1176-1181 (2008)). This results inpreferential attachment of the DNA polymerase molecules to the exposedsilica in the holes of the aluminum coating. This setup allowsevanescent wave phenomena to be used to reduce fluorescence background,allowing the use of higher concentrations of fluorescently labeleddNTPs. The fluorophore is attached to the terminal phosphate of thedNTPs, such that fluorescence is released upon incorporation of thedNTP, but the fluorophore does not remain attached to the newlyincorporated nucleotide, meaning that the complex is immediately readyfor another round of incorporation. By this method, incorporation ofdNTPs into an individual primer-template complexes present in the holesof the aluminum coating can be detected. See, e.g., Eid et al., Science323, 133-138 (2009).

Sequencing Template; Amount of Sequencing Data Obtained

In some embodiments, sequence data is obtained directly from a circularnucleic acid molecule, that is, by using the circular nucleic acidmolecule as a template. The circular nucleic acid molecule used as atemplate can be a circular pair-locked molecule. In some embodiments,sequence data is obtained from a product nucleic acid molecule thatitself was synthesized using a circular nucleic acid molecule as atemplate; that is, a template from which sequence data is obtained canbe a product nucleic acid molecule synthesized from a circular nucleicacid molecule template. In some embodiments, sequence data is obtainedfrom both a circular nucleic acid molecule template and from a productnucleic acid molecule synthesized from the circular nucleic acidmolecule template.

In some embodiments, rolling circle amplification, comprisingsynthesizing a product nucleic acid molecule comprising at least twoinsert-sample units using the circular nucleic acid molecule as atemplate, is performed. In some embodiments, the rolling circleamplification comprises synthesizing a product nucleic acid moleculecomprising at least 3, 4, 5, 10, 15, 20, 25, 50, or 100 insert-sampleunits. The use of rolling circle amplification to produce a number ofcopies of a template is well known in the art; see, e.g., Blanco et al.,J Biol Chem 264, 8935-8940 (1989) and Banér et al., Nucleic Acids Res26, 5073-5078 (1998). The rolling circle amplification can be performedas part of sequencing in which the circular nucleic acid molecule is thesequencing template, or to synthesize a product nucleic acid moleculewhich is to be used as a sequencing template.

Regardless of the template, the sequence data obtained according to themethods of the invention comprises at least two repeats of the nucleicacid sample sequence; these at least two repeats can include, in someembodiments, at least one forward repeat of the nucleic acid samplesequence and at least one reverse repeat of the nucleic acid samplesequence. In some embodiments, the sequence data comprise at least 3, 4,5, 10, 15, 20, 25, 50, or 100 repeats of the nucleic acid samplesequence. In some embodiments, the sequence data comprise at least 2, 3,4, 5, 10, 15, 20, 25, 50, or 100 forward repeats of the nucleic acidsample sequence. In some embodiments, the sequence data comprise atleast 2, 3, 4, 5, 10, 15, 20, 25, 50, or 100 reverse repeats of thenucleic acid sample sequence. In some embodiments, the sequence datacomprise at least 2, 3, 4, 5, 10, 15, 20, 25, 50, or 100 each of forwardand reverse repeats of the nucleic acid sample sequence.

Calculating Scores

In some embodiments, the methods of the invention comprise calculatingscores of the sequences of at least two inserts in the sequence data bycomparing the sequences to the known sequence of the insert. Inembodiments in which the sequence of the insert is only partially orinexactly known, the known sequence of the nucleic acid insert cancomprise ambiguous or unknown positions, for example, through use ofambiguity codes or a position weight matrix.

Comparing the sequences to the known sequence of the insert includesidentifying the sequences of at least two inserts in the sequence data.Identifying the sequences can be done in some embodiments by visualinspection, i.e., by a person visually scanning the sequence data andspotting the insert nucleic acid sequences contained therein, or by acomputer-aided alignment method. See, e.g., International PatentApplication Publication WO 2009/017678. In some embodiments, identifyingthe sequences can be done by scanning the sequence data using analgorithm that recognizes the sequences, for example, by calculatingscores iteratively or heuristically for multiple positions within thesequence data in order to identify local extrema that correspond mostclosely to the known sequence of the nucleic acid insert. In someembodiments, identifying the sequence of the at least two nucleic acidinserts is performed simultaneously with calculating the scores, in thatboth processes can utilize the same score.

In some embodiments, calculating scores comprises performing analignment using an appropriate alignment algorithm, of which many areknown in the art and are readily available, for example, BLAST,MEGABLAST, Smith-Waterman alignment, and Needleman-Wunsch alignment.See, e.g., Altschul et al., J Mol Biol 215, 403-410 (1990). Appropriatealignment algorithms include both algorithms allowing gaps andalgorithms that do not allow gaps. Alternatively, in some embodiments,calculating scores comprises analyzing the sequences using an algorithmsuch as running a position weight matrix over the sequences andcalculating the sum of the elements of the matrix corresponding to thesequence. In this way, the score can be calculated as the local maximumfound by applying the matrix to a sequence read in a stepwise fashion.

In some embodiments, the scores are positively correlated with thecloseness of the at least two nucleic acid insert sequences to the knownsequence (e.g., the maximum possible score results from an exact match).Such positively correlated scores include, without limitation, percentidentity, bit scores, and matching base count.

In some embodiments, the scores are negatively correlated with thecloseness of the at least two nucleic acid insert sequences to the knownsequence (e.g., the minimum possible score results from an exact match).Such negatively correlated scores include, without limitation, e-value,number of mismatches, number of mismatches and gaps, percent mismatched,and percent mismatched/gapped.

In some embodiments, the scores are calculated on a rate basis. Thepossible range of scores calculated on a rate basis does not change as afunction of the length of the sequences being compared. Examples ofscores calculated on a rate basis include, without limitation, percentidentity and percent mismatched/gapped.

In some embodiments, the scores are calculated on a count basis. Thepossible range of scores calculated on a count basis changes as afunction of the length of the sequences being compared. Examples ofscores calculated on a count basis include, without limitation, bitscores, number of mismatches, number of mismatches and gaps, andmatching base count.

Accepting or Rejecting Repeats of the Sequence of the Nucleic AcidSample; Accepted Sequence Set

In some embodiments, the methods of the invention comprise accepting orrejecting repeats of the sequence of the nucleic acid sample in thesequence data according to the scores of one or both of the sequences ofthe inserts immediately upstream and downstream of the repeat of thesequence of the nucleic acid sample. Thus, in various embodiments, thescores of both the immediately upstream and immediately downstreamnucleic acid inserts, the score of either one, or the score of one orthe other specifically is/are used to decide whether to accept or rejecta nucleic acid sample sequence in the sequence data.

In embodiments in which the scores are positively correlated with thecloseness of the at least two nucleic acid insert sequences to the knownsequence, scores are required to be greater than, or greater than orequal to, a threshold value in order to accept a sequence. The choice ofan appropriate threshold value depends on multiple factors, includingthe type of score being used, the error rate of the sequencing method,and time and redundancy considerations.

Accepting and rejecting repeats of the sequence of the nucleic acidsample can be implemented in various ways such that at least oneaccepted repeat is used, and any rejected repeats are not used, todetermine the sequence of the nucleic acid sample. Accepting andrejecting repeats may or may not be performed in a concerted manner withcompiling an accepted sequence set. For example, the sequences ofaccepted repeats can be copied as they are accepted into a new datastructure, which becomes the accepted sequence set. Or, the sequences ofrejected repeats can be deleted or overwritten (e.g., with ‘0’ or ‘X’characters that represent null or excluded data) as they are rejected;in this case, once the rejected sequences have been deleted oroverwritten, the original data structure has been modified so as tobecome the accepted sequence set. In these examples, accepting andrejecting repeats is considered to be performed in a concerted mannerwith compiling an accepted sequence set.

In some embodiments, repeats of the sequence of the nucleic acid samplecan be rejected on an additional basis, such as having a length thatdeviates from the length of other repeats of the sequence of the nucleicacid sample (see, e.g., FIG. 7B). For example, a repeat of the sequenceof the nucleic acid sample can be rejected if it deviates to a thresholdextent from the mean or median length of the other nucleic acid samplesequences, or of a preliminary version of the accepted sequence setcomprising repeats of the sequence of the nucleic acid sample acceptedaccording to the scores of one or both of the sequences of the insertsimmediately upstream and downstream of the repeat of the sequence of thenucleic acid sample as described above, which may or may not have therepeat of the sequence of the nucleic acid sample under considerationfor possible rejection temporarily removed for calculation of the medianor mean length. The threshold extent can be expressed in terms ofabsolute length, for example, 1, 2, 5, 10, 20, or 50 nucleotides;relative length, for example, 1%, 2%, 5%, 10%, 20%, or 50%; or in termsof a statistical measure, such as standard deviation, for example, 0.5,1, 1.5, 2, 2.5, 3, 3.5, 4, or 5 standard deviations.

Alternatively, the sequences can be flagged as accepted or rejected, andthen after the flagging process is complete, the accepted sequences canbe copied into a new data structure, or the rejected sequences can bedeleted or overwritten, to generate an accepted sequence set in anon-concerted manner.

The accepted sequence set can be chosen from forms including a singledata string, which comprises the at least one accepted repeat of thesequence of the nucleic acid sample and any additional accepted repeatsin concatenated form, and a multi-element variable, in which eachelement represents an accepted repeat of the sequence of the nucleicacid sample or a subpart thereof. In some embodiments, the multi-elementvariable is chosen from a list, array, hash, and matrix. Any form ofdata structure allowing for storage of the at least one accepted repeatof the sequence of the nucleic acid sample and subsequent determinationof the sequence of the nucleic acid sample is suitable for use.

In embodiments in which the form of the accepted sequence set differsfrom the form of the raw sequence data (e.g., the raw sequence data isin the form of a string and the accepted sequence set is in the form ofa multi-element data structure such as an array), the raw sequence datacan be parsed into elements containing repeats, insert-sample units, orsample repeats flanked by the immediately upstream and downstreaminserts at a point in the method after the raw sequence data is obtainedand before the final accepted sequence set is generated. This parsingstep can occur before or after the scoring step discussed above.

Determining the Sequence of the Nucleic Acid Sample; ConsensusSequences; Confidence Levels

In some embodiments, the methods comprise determining the sequence ofthe nucleic acid sample.

The mode of determining the sequence of the nucleic acid sample can bechosen conditionally based on the number of repeats of the nucleic acidsample in the accepted sequence set. For example, when the acceptedsequence set contains only one accepted repeat, the sequence of thenucleic acid sample can be determined to be the sequence of the acceptedrepeat. When the accepted sequence set contains only two, or at leastthree, accepted repeats, the sequence of the nucleic acid sample can bedetermined to be the consensus sequence (see below) of the acceptedrepeats. More options for how the consensus sequence is determined areavailable when the accepted sequence set contains at least threeaccepted repeats.

Consensus Sequence

The consensus sequence is determined from an alignment (performed asdiscussed above, in the “Calculating scores” section) of the acceptedrepeats; at positions in the alignment where the accepted repeatscontain the same base, the consensus sequence contains that base. Insome embodiments, at positions in the alignment where the acceptedrepeats do not contain the same base, the consensus sequence containsthe appropriate ambiguity code (e.g., R when the accepted repeatscontain A and G at a position). In some embodiments, at positions in thealignment where the accepted repeats do not contain the same base, theconsensus sequence contains an N or other symbol indicative of anunknown base. In some embodiments, at positions in the alignment wherethe accepted repeats do not contain the same base, the consensussequence contains the base from the accepted repeat that gave a strongeror more robust signal during acquisition of the sequence (e.g., if theraw data were in the form of fluorescence, the base which was calledbased on brighter fluorescence emission (in some embodiments, afterappropriate normalization and/or standardization) is placed in theconsensus sequence.

When a consensus sequence is determined from an accepted sequence setcontaining at least three accepted repeats, the base at each position ofthe consensus sequence can in some embodiments be determined by majorityvote; i.e., the base present at a position in more than half of theaccepted repeats is placed at that position in the consensus sequence.When the accepted repeats disagree at a position such that there is nomajority vote at that position, the base at that position in theconsensus sequence is determined by another method, for example, theplurality vote can be used (i.e., the base most frequently present at aposition in of the accepted repeats is placed at that position in theconsensus sequence), or one of the procedures discussed in the precedingparagraph can be used.

In some embodiments, when a consensus sequence is determined from anaccepted sequence set containing at least three accepted repeats, thebase at each position of the consensus sequence can in some embodimentsbe determined according to the frequency of each base at that positionin the accepted repeats. Thus, the consensus sequence can be aprobabilistic representation of the likelihood that each base is presentat each position in the nucleic acid sample. Such a representation cantake the form of a position weight matrix. In some embodiments, theelements of the position weight matrix are the frequencies with whicheach base was observed at each position in the alignment of the acceptedrepeats.

In some embodiments, the elements of the position weight matrix arecalculated from the frequencies with which each base was observed ateach position in the alignment of the accepted repeats; other factorscan also be used in this calculation, for example, when some acceptedrepeat sequences were acquired with stronger or more robust signalsduring acquisition of the sequence than other repeats, the acceptedrepeat sequences can be given more weight, and/or the other repeats canbe given less weight. The degree to which the weights are modified canbe quantitatively determined, based, for example, on the signalstrength, or it can be a fixed modification; for example, the weight ofbases acquired with a relatively strong signal can be increased by avalue such as 50% or 100%, and/or the weight of bases with a relativelyweak signal can be reduced by a value such as 33% or 50%.

In some embodiments, the elements of the position weight matrix arevalues which have been derived from transformed frequencies of each baseat each position (possibly weighted as discussed above). Frequencies canbe transformed, for example, logarithmically or by exponentiation; insome embodiments, the transformation has the effect of down weightingbases rarely observed at a position and/or up weighting the base orbases commonly observed at a position. For example, if T is present at aposition in an alignment of N accepted repeat sequences M times, whereN>2 and M<N/2, and C is present every other time (i.e., N−M times), insome embodiments the transformation of these frequencies would result inthe weight of T in the position weight matrix being less than M/N (orthe percentage corresponding thereto) and/or the weight of C beinggreater than (N−M)/N (or the percentage corresponding thereto). In someembodiments, the transformation is chosen so as to only up weight themost commonly observed base (or bases in the case of a tie infrequency).

Confidence Levels

In some embodiments, a confidence level is determined for at least oneposition in the sequence of the nucleic acid sample. A confidence levelcan be expressed in a number of ways, for example, as an overall basecall accuracy value, expressed as a percentage or as a phred score, oras an error rate. In some embodiments, the confidence level isdetermined from the frequency of the most common base or bases at aposition, or of the combined frequency of the bases that are not themost common. In some embodiments, these frequencies are transformed, upweighted, and/or down weighted as discussed above.

Determining a Confidence Level of the Sequence as a Whole; Determiningthe Sequence of the Nucleic Acid Sample and Confidence Levels in RealTime and/or to a Desired Level of Confidence

In some embodiments, the methods of the invention comprise determining aconfidence level of the sequence as a whole. The confidence level of thesequence as a whole can be expressed in a number of ways, for example,as an overall base call accuracy value, expressed as a percentage or asa phred score; as an error rate; or as an expected number of errors inthe sequence.

Confidence levels from the individual positions, as discussed in theabove section, can be used to calculate the confidence level of thesequence as a whole. For example, an overall confidence level can bedetermined as the arithmetic mean, geometric mean, median, or modalconfidence level of the statistical population of confidence levels ateach position of the sequence of the nucleic acid sample. In someembodiments, the statistical population of confidence levels at eachposition of the sequence of the nucleic acid sample is processed priorto calculation of the confidence level of the sequence as a whole, forexample, to reject outliers.

In some embodiments, the methods of the invention comprise determiningthe sequence of the nucleic acid sample and confidence levels in realtime. In these embodiments, data acquired in the sequencing step isprocessed to determine sequence and confidence levels concurrently withthe acquisition of additional sequence data, e.g., from additionalrepeats of a rolling circle amplification product. As the additionalsequence data is acquired, both the determined sequence and theconfidence levels are updated. In some embodiments, the real timeprocess is continued until a preselected confidence level is reached.The preselected confidence level can be, for example, a base callaccuracy of 90%, 95%, 99%, 99.5%, 99.9%, 99.95%, or 99.99%. Thepreselected confidence level can be for the sequence as a whole or afraction of the positions in the sequence, and can be chosen from valuessuch as, for example, 50%, 67%, 75%, 80%, 85%, 90%, 95%, 98%, 99%,99.5%, and 99.9%.

Multiple Samples; Assembling a Contig

In some embodiments, the method comprises repeating the steps of themethod using at least one other sample from the same source, species, orstrain as the nucleic acid sample that has a sequence, that partiallyoverlaps the sequence of the nucleic acid sample, thereby determining atleast one other sequence, and assembling the at least one other sequencewith the sequence of the original sample to form a contig. In someembodiments, the method comprises repeating the steps of the method withmany samples, so as to generate contigs of sizes greater than 0.5, 1, 2,5, 10, or 100 kb, or 1, 2, 5, 10, 100, or 1,000 Mb. In some embodiments,the contig represents the complete sequence, or the complete sequenceexcept for heterochromatic or refractory regions, of a nucleic acidmolecule, which may be, for example and without limitation, achromosome, minichromosome, artificial chromosome, viral genome, orextrachromosomal element. Contig assembly can be carried out usingmethods known in the art.

Modified Bases

In some embodiments, the nucleic acid sample comprises at least onemodified base, for example, 5-methylcytosine, 5-bromouracil, uracil,5,6-dihydrouracil, ribothymine, 7-methylguanine, hypoxanthine, orxanthine. Uracil can be considered a modified base in a DNA strand, andribothymine can be considered a modified base in an RNA strand. In someembodiments, at least one modified base in the double-stranded nucleicacid sample is paired with a base that has a base pairing specificitydifferent from the preferred partner base(s) of the modified base. Thiscan occur, for example, when one base in a double stranded molecule hasundergone a reaction (e.g., due to sporadic oxidation, or exposure to amutagenizing agent such as radiation or a chemical mutagen) thatconverted it from one of the standard bases to a modified base that doesnot have the same preferred partner base(s).

Preferred partner bases are based on Watson-Crick base pairing rules.For example, the preferred partner base of adenine is thymine (oruracil), and vice versa; the preferred partner base of cytosine isguanine, and vice versa. Preferred partner bases of modified bases aregenerally known to those of skill in the art or can be predicted basedon the presence of hydrogen bond donors and acceptors in positionsanalogous to those of the standard bases. For example, hypoxanthine hasa hydrogen bond acceptor (a double-bonded oxygen) in the 6 position ofthe purine ring, like guanine, and therefore its preferred partner baseis cytosine, which has a hydrogen bond donor (an amine group) in the 6position of the pyrimidine ring. Notably, hypoxanthine can be formed bydeamination of adenine. As adenine would normally be paired with thyminein DNA, this deamination reaction can result in a hypoxanthine-thyminepair, in which the modified base hypoxanthine is not paired to itspreferred partner base. Cytosine can also be deaminated to form uracil.In the context of DNA, uracil can be considered a modified base, and ifit is paired to guanine (as can result from cytosine deamination innormal double-stranded DNA), then this is also a situation where themodified base uracil is not paired to its preferred partner base.

Detection of Modified Bases; Altering the Base Pairing Specificity ofBases of a Specific Type

In some embodiments, the methods of the invention comprise altering thebase pairing specificity of bases of a specific type. Altering the basepairing specificity of bases of a specific type can comprisespecifically altering the base pairing specificity of an unmodifiedversion of a base, e.g., cytosine. In this case, the base pairingspecificity of at least one modified form of the base, for example,5-methylcytosine, is not altered.

Alternatively, altering the base pairing specificity of bases of aspecific type can comprise specifically altering the base pairingspecificity of a modified version of a base (e.g., 5-methylcytosine),but not the unmodified version of the base (cytosine).

In some embodiments, altering the base pairing specificity of bases of aspecific type comprises photochemical transition, which converts5-methylcytosine (but not unmodified cytosine) to thymine. See, e.g.,Matsumura et al., Nucleic Acids Symp Ser No. 51, 233-234 (2007). Thisreaction alters the base pairing specificity of the bases undergoingphotochemical transition from guanine to adenine (guanine pairs with5-methylcytosine while adenine pairs with thymine).

In other embodiments, altering the base pairing specificity of bases ofa specific type comprises bisulfite conversion, which converts cytosine(but not 5-methylcytosine) to uracil. See, e.g., Laird et al., Proc NatlAcad Sci USA 101, 204-209 (2004), and Zilberman et al., Development 134,3959-3965 (2007). This reaction alters the base pairing specificity ofthe bases undergoing bisulfite conversion from guanine to adenine(guanine pairs with cytosine while adenine pairs with uracil).

In still other embodiments, modified bases can be detected without analteration step, such as in cases where the modified base has alteredbase pairing specificity relative to the unmodified version of the base.Examples of such bases may include 5-bromouracil, uracil,5,6-dihydrouracil, ribothymine, 7-methylguanine, hypoxanthine, andxanthine. See, e.g., Brown, Genomes, 2^(nd) Ed., John Wiley & Sons,Inc., New York, N.Y., 2002, chapter 14, “Mutation, Repair, andRecombination,” discussing the propensity of 5-bromouracil to undergoketo-enol tautomerization which results in increased pairing to guaninerelative to adenine, and the formation of hypoxanthine (which pairspreferentially to cytosine over thymine) by deamination of adenine.

Nucleotide Analog that Discriminates Between a Base and its ModifiedForm

In some embodiments, sequence data is obtained using at least onenucleotide analog that discriminates between a base and its modifiedform (a “discriminating analog”; it pairs preferentially with one butnot the other of the base and its modified form). The nucleotide analogcan be used and detected as though it is a fifth base in addition to thestandard four bases, for example, by use of differential labels inreversible terminator sequencing or ligation sequencing, or when it isincorporated in pyrosequencing, in which nucleotides can be added one ata time and then washed away. In some embodiments, the discriminatinganalog is added before its corresponding natural nucleotide (e.g., inpyrosequencing) or provided in a concentration ranging from 10 to100-fold higher than the concentration of its cognate natural nucleotide(e.g., in reversible terminator sequencing). For example, thediscriminating analog can be an analog of deoxyguanosine triphosphatethat discriminates between cytosine and 5-methylcytosine (e.g., it willpair with cytosine but not 5-methylcytosine); the analog can be providedat a concentration ranging from 10 to 100-fold higher than theconcentration of deoxyguanosine triphosphate. In this way, the analogshould generally be incorporated opposite the version of the base itpreferentially pairs with, but the natural base should generally beincorporated opposite the version of the base that the analog does notpreferentially pair with.

Examples of discriminating analogs can be found in U.S. Pat. No.7,399,614, and include, for instance, the following molecules, whichdiscriminate between unmodified cytosine and 5-methylcytosine, in thatthey preferentially pair with the former:

These molecules are referred to as Discriminating Analog 1 andDiscriminating Analog 2, respectively.

Determining the Positions of Modified Bases in the Nucleic Acid Sample

In some embodiments, the methods of the invention comprise determiningthe positions of modified bases in the nucleic acid sample. Theseembodiments comprise (i) providing the nucleic acid sample indouble-stranded form; (ii) converting the nucleic acid sample into acircular pair-locked molecule, wherein the circular pair-locked moleculecomprises forward and reverse repeats of the sequence of the nucleicacid sample and two nucleic acid inserts having known sequences, whichmay be identical or non-identical; (iii) optionally altering thebase-pairing specificity of bases of a specific type in the circularpair-locked molecule; (iv) then, obtaining sequence data templated bythe forward and reverse repeats of the circular pair-locked molecule orby a complementary sequence thereof; and (v) determining the positionsof the modified bases in the nucleic acid sample using the sequence dataof at least the forward and reverse repeats or copies thereof. Notably,sequence templated by a forward repeat will have the same sense as thereverse repeat (and vice versa), but may or may not be completelyidentical to the reverse repeat; differences can result from the forwardrepeat containing bases that can pair to a base other than thecorresponding base in the reverse repeat. An example of such a situationis if the forward repeat in a cPLM contains 5-bromouracil which had beenpaired to an adenine in the reverse strand but templates the addition ofa guanine in a sequencing-by-synthesis reaction.

Sequence data are obtained comprising at least two repeats: at least oneof a repeat of the sample (e.g., the repeat labeled 17 in FIG. 5A) and arepeat of the newly synthesized complement of the forward strand (e.g.,the repeat labeled 21 in FIG. 6A); and at least one of a repeat of thenewly synthesized complement of the reverse strand (e.g., the repeatlabeled 19 in FIG. 6A) and a repeat of the reverse strand (e.g., therepeat labeled 16 in FIG. 6A). These repeats are aligned. The alignmentcan be performed using any appropriate algorithm, as discussed above. Aposition at which there is disagreement among the repeats (e.g., theposition labeled 41 in FIG. 6B) signifies that a base in the nucleicacid sample at that position underwent alteration of its base pairingspecificity. Depending on the type of modification, modified base,and/or discriminating analog used in the process or present in thesample, the bases originally present at the corresponding position ofthe nucleic acid sample can be determined.

For example, where the circular pair locked molecule has been altered byconversion of ^(m)C to T (see FIG. 5A), the disagreement indicates thata ^(m)C was present in the nucleic acid sample at the position that is aT or complementary to an A in one read, and is a C or complementary to aG in another read; the logic is that at a position where the sequencesdisagree, the base which is the product of the conversion reaction, T,has replaced the substrate of the conversion reaction, ^(m)C, which waspresent in the nucleic acid sample.

In another example, where the circular pair locked molecule has beenaltered by conversion of C to U, the disagreement indicates that a C waspresent in the nucleic acid sample at the position occupied by that is aU or T, or is complementary to an A in one read, and is a C orcomplementary to a G in another read; the logic is that at a positionwhere the sequences disagree, the base which is the product of theconversion reaction, U (which may be read by the sequencing system as aT), has replaced the substrate of the conversion reaction, C, which waspresent in the nucleic acid sample. As ^(m)C residues would not bechanged by conversion of C to U, the positions where the reads are inagreement in showing C at a position and/or G as its complement indicatethat ^(m)C was present at this position in the original sample.

In embodiments in which a discriminating analog was used as discussedabove, the presence of the base it preferentially binds to can beinferred in the original sequence at the position of the originalsequence corresponding to the position where the discriminating analogappears.

System/Computer Readable Medium

In some embodiments, the invention relates to a system comprising asequencing apparatus operably linked to a computing apparatus comprisinga processor, storage, bus system, and at least one user interfaceelement. The user interface element can be chosen from a display, akeyboard, and a mouse. In some embodiments, the system comprises atleast one integrated circuit and/or at least one semiconductor.

In some embodiments, the sequencing apparatus is chosen from sequencingapparatuses configured to perform at least one of the sequencing methodsdiscussed above.

In some embodiments, the display can be a touch screen, serving as thesole user interface element. The storage is encoded with programmingcomprising an operating system, user interface software, andinstructions that, when executed by the processor on a system comprisinga sequencing apparatus operably linked to a computing apparatuscomprising a processor, storage, bus system, and at least one userinterface element, optionally with user input, perform a method of theinvention as described above. In some embodiments, the storage furthercomprises sequence data, which can be in any of the forms discussedabove, for example, raw sequence data, an accepted sequence set, aconsensus sequence, etc.

In some embodiments, the storage and all of its contents are locatedwithin a single computer. In other embodiments, the storage is dividedbetween at least two computers, for example, computers linked via anetwork connection. In some embodiments, the user interface is part ofone computer which is in communication with at least one other computercomprising at least one component of the system, for example, theprocessing software.

In some embodiments, output of a system or a method executed by aprocessor results in an indication that there is a modified base in atleast one position in a nucleic acid sample. The indication can be inany number of forms, for example, a list of the modified positions inthe sequence, a textual or graphical representation of the sequencewherein the modified positions are highlighted or marked, such as withan asterisk or similar character or with bold, italic, or underlineformatting, colored text, or a depiction of the chemical structure ofthe nucleic acid including the structure of the modified base.

EXAMPLES

The following specific examples are to be construed as merelyillustrative, and not limitative of the remainder of the disclosure inany way whatsoever. Without further elaboration, it is believed that oneskilled in the art can, based on the description herein, utilize thepresent invention to its fullest extent.

Example 1 Rolling Circle Amplification of a Synthetic CircularPair-Locked Molecule

Four oligodeoxyribonucleotides were provided, as shown in Table 1.

TABLE 1 Oligonucleotide sequences SEQ ID Name Sequence NO CPLM-1CGACTTATGCATTTGGTATCTGCGCTCTGC 1 ATATTTAAATGGAAGGAGATAGTTAAGGATAAGGGCAGAGCGCAGATAC CPLM-2 CAAATGCATAAGTCGTGTCTTACCGGGTTG 2ATAGCGGCCGCTCGGAGAAAAGAAGTTGG ATGATGCAACCCGGTAAGACA pS-T1CCTTATCCTTAACTATCTCCTT 3 pS-T2 TAGCGGCCGCTCGGAGAAAAG 4

CPLM-1 and CPLM-2 were phosphorylated in separate 50 μL reactions inwhich 30 μL of 10 μM oligodeoxyribonucleotide (final concentration) wastreated with 1 μL of 10 U/μL T4 polynucleotide kinase (New EnglandBiolabs (“NEB”) Cat. No. M0201S), in the presence of 5 μL 10×T4 ligasebuffer (NEB; the 10× stock buffer contains 10 mM ATP). 14 μL ddH₂O wereadded to give a final volume of 50 μL (see Table 2). The reactions wereincubated at 37° C. for 30 min, followed by enzyme inactivation at 65°C. for 20 min.

TABLE 2 Phosphorylation reaction conditions (volumes in μL) Reagent5′P-CPLM-1 5′P-CPLM-2 10 uM CPLM-1 30 0 10 uM CPLM-2 0 30 10 u/uL T4 PNK1 1 10 X T4 Ligase buffer 5 5 ddH₂O 14 14 Total volume 50 50

The concentration of phosphorylated CPLM-1 and CPLM-2 (5′P-CPLM-1 and5′P-CPLM-2, respectively) from the above reactions was adjusted to 6 μM.

Phosphorylated CPLM-1 and CPLM-2 were then denatured at 95° C. for 5min, then placed on ice and mixed with buffer, ddH₂O, and T4 ligase(NEB, Cat. No. M0202S) to produce circular pair-locked molecules, asshown in Table 3. The ligation occurred at 25° C., and 18 μL aliquotswere removed at 10, 30 and 60 min. A negative control with no ligase wasrun in parallel (L0 column in Table 3).

TABLE 3 Ligation reaction conditions Reagent L0 L3 6 μM 5′P-CPLM-1 9 9 6μM 5′P-CPLM-2 9 9 400 u/μL T4 Ligase 0 3 10 X buffer 6 6 ddH₂O 36 33Total volume 60 60

The ligation products were combined with pS-T1 and/or pS-T2 primers,dNTPs, RepliPHI™ Phi29 DNA polymerase (Epicentre, Cat. No. PP031010),and an appropriate 10× reaction buffer RepliPHI Phi29 DNA Polymerasebuffer as shown in Table 4.

TABLE 4 Rolling circle amplification of circular pair-locked moleculesControls 2-primed 1-primed Reagent C1 C2 L0 L3 L0 L3 10 mM dNTP 5 5 5 55 5 10 μM pS-T1 primer 0 0 6 6 0 0 10 μM pS-T2 primer 0 0 6 6 6 6 1XL0_10, 30, 60 min 1 0 1 0 1 0 1X L3_10, 30, 60 min 0 1 0 1 0 1 1000 u/μLphi29 polymerase 1 1 1 1 1 1 10X buffer 5 5 5 5 5 5 ddH₂O 38 38 26 26 3232 Total volume 50 50 50 50 50 50

The reactions were assembled without Phi29 polymerase, denatured at 95°C. for 5 min, and placed on ice for 5 min. Phi29 polymerase was addedfollowed by incubation at 30° C. for 18 hours.

5 μL samples of reaction products were mixed with 1 μL 6× loading dye(0.03% bromophenol blue, 0.03% xylene cyanol FF, 60% glycerol, 100 mMTris-EDTA (pH 7.6)), heated at 95° C. for 10 min, and then placed on iceimmediately. A second set of reaction product samples was treatedidentically except that 1% SDS was added as well.

Samples were loaded into a 0.7% agarose gel in 1×TAE buffer andelectrophoresed at 135 V for 28 min. DNA was visualized using GelRed™precast gel staining (Biotium, Cat. No.: 41003 GelRed™ Nucleic Acid GelStain, diluted 10,000× in water). The gel is shown in FIG. 9. Rollingcircle amplification products with apparent molecular weights greaterthan 10 kb were observed in the samples from reactions using L3 ligationreaction products and both pS-T1 and pS-T2 primers, but not the samplesusing the L0 controls or the samples that lacked a primer. The samplesusing L3 ligation reaction products and both pS-T1 and pS-T2 primersthat were treated with SDS showed greater retention of product in thewells, consistent with denaturation of secondary structure in the RCAproducts.

Example 2 Simulation of Detection of Methylation Using Conversion of Cto U by Bisulfite Treatment with a Linear Pair-Locked Molecule

Determination of the sequence and 5-methylcytosine positions of ahypothetical duplex DNA fragment using conversion of C residues to Uresidues by bisulfite treatment is simulated as follows. The generalscheme of this Example is illustrated in FIG. 12. The sequence of theDNA is shown below.

The two strands are connected by ligation to a linker sequence(represented as “nnnn”) to give the following product. The linkersequence is suitable for use as a sequencing primer.

(SEQ ID NO: 7)3′-TCTACACCTG^(m)CCCCACCCG^(m)CCTCCACCCAACCCCGnnnnCGGGGTTGGGTGGAGG^(m)CGGGTGGGG^(m)CAGGTGTAGA-5′

Additionally, a linear flap of known sequence (not shown) is attached toeach end of the molecule of SEQ ID NO:7. The flap at the 3′ end issuitable for primer binding for sequencing or replication. Thecomplement of the flap at the 5′ end is suitable for primer binding forsequencing or replication.

The product is treated with sodium bisulfite, resulting in theconversion of cytosine (but not 5-methylcytosine) residues to uracil,giving the following product. The newly formed uracil residues arebolded and marked with asterisks above the bases.

(SEQ ID NO: 8)     *  * **    *** ***  * ** ***  ****     *3′-TUTAUAUUTG^(m)CUUUAUUUG^(m)CUTUUAUUUAAUUUUGnnnnUGGGGTTGGGTGGAGG^(m)CGGGTGGGG^(m)CAGGTGTAGA-5′

A complementary strand (labeled SEQ ID NO: 9 below) is synthesized viaDNA replication involving annealing of a primer to the flap added to the3′ end.

The above duplex is sequenced in both directions; sequencingintermediates are shown below. The nascent strand, whose sequence isbeing obtained, is SEQ ID NO: 10 in reaction a and SEQ ID NO: 11 inreaction b.

Thus, the reads predicted to be obtained from these reactions containthe following sequences.

(SEQ ID NO: 10) a: 5′-AGATGTGGACGGGGTGGGCGGAGGTGGGTTGGGGTnnnn-3′(SEQ ID NO: 11) b: 5′-AAATATAAACGAAATAAACGAAAATAAATTAAAACnnnn-3′

The sequence of the original sample, including cytosine methylationstatus, is determined by applying the following rules, summarized inTable 5. The forward strand of the original sequence is the strand withthe same sense as the two reads.

At positions where read a and read b both have A, the forward strand ofthe original sequence also has A, and the reverse strand has T. Atpositions where read a and read b both have T, the forward strand of theoriginal sequence also has T, and the reverse strand has A.

When read a and read b both have C, then the forward strand of theoriginal sequence has ^(m)C, and the reverse strand has G. When read aand read b both have G, then the forward strand of the original sequencehas G, and the reverse strand has ^(m)C.

When one read has G at a position where the other read has A, theforward strand of the original sequence has G, and the reverse strandhas C.

When one read has T at a position where the other read has C, theforward strand of the original sequence has C, and the reverse strandhas G.

Reads a and b are matched to column 1 and 2 in Table 5 according towhich read contains G and T residues at the positions where the readsdiffer; in this example, read a corresponds to column 1.

TABLE 5 Bisulfite treatment methylation status determination rulesOriginal sequence Sequencing reads Forward strand Reverse Strand 1 2 (5′=> 3′) (3′ => 5′) A A A T T T T A C C C methylated G G G G C methylatedG A G C T C C G

Application of the above rules to SEQ ID NOs: 10 and 11 results inrecovery (after removal of the linker sequence nnnn) of the originalsequences, i.e., SEQ ID NOs: 5 and 6. An alignment of reads a and b withthe forward strand of the original sequence is shown in FIG. 10A.

Example 3 Simulation of Detection of Methylation Using Conversion of mCto T by Photochemical Transition with a Linear Pair-Locked Molecule

Determination of the sequence and 5-methylcytosine positions of ahypothetical duplex DNA fragment using conversion of ^(m)C to T byphotochemical transition is simulated as follows. The general scheme ofthis Example is shown in FIG. 13. The sequence of the DNA is shownbelow.

The two strands are connected by ligation to a linker sequence(represented as “nnnn”) to give the following product. The linkersequence is suitable for use as a sequencing primer. Linear flaps (notshown) are also attached to the 3′ and 5′ ends of this molecule.

(SEQ ID NO: 7)3′-TCTACACCTG^(m)CCCCACCCG^(m)CCTCCACCCAACCCCGnnnnCGGGGTTGGGTGGAGG^(m)CGGGTGGGG^(m)CAGGTGTAGA-5′

The product is treated with light so as to photochemically convert5-methylcytosine (but not cytosine) residues to thymine, giving thefollowing product. The newly formed thymine residues are bolded andmarked with asterisks above or below the bases.

(SEQ ID NO: 12)             *        *                                   *3′-TCTACACCTGTCCCACCCGTCTCCACCCAACCCCGnnnnCGGGGTTGGGTGGAGGTGGGTGGGGTAGGTGTAGA-5′     *

A complementary strand (labeled SEQ ID NO: 13 below) is synthesized viaDNA replication using a primer that binds to the flap attached to the 3′end of the molecule.

The above duplex is sequenced in both directions as in Example 2 above,obtaining the following reads.

Read a: (SEQ ID NO: 14) 5′-AGATGTGGATGGGGTGGGTGGAGGTGGGTTGGGGC-3′Read b: (SEQ ID NO: 15) 5′-AGATGTGGACAGGGTGGGCAGAGGTGGGTTGGGGC-3′

The sequence of the original sample, including cytosine methylationstatus, is determined by applying the following rules, summarized inTable 6. The forward strand of the original sequence is the strand withthe same sense as the two reads.

At positions where read a and read b both have A, the forward strand ofthe original sequence also has A, and the reverse strand has T. Atpositions where read a and read b both have T, the forward strand of theoriginal sequence also has T, and the reverse strand has A.

When read a and read b both have C, then the forward strand of theoriginal sequence has C, and the reverse strand has G. When read a andread b both have G, then the forward strand of the original sequence hasG, and the reverse strand has C.

When one read has G at a position where the other read has A, theforward strand of the original sequence has G, and the reverse strandhas ^(m)C.

When one read has T at a position where the other read has C, theforward strand of the original sequence has ^(m)C, and the reversestrand has G.

Reads a and b are matched to column 1 and 2 in Table 6 according towhich read contains G and T residues at the positions where the readsdiffer; in this example, read a corresponds to column 1.

TABLE 6 Photochemical transition methylation status determination rulesOriginal sequence Sequencing reads Forward strand Reverse strand 1 2 (5′=> 3′) (3′ => 5′) A A A T T T T A C C C G G G G C G A G C methylated T CC methylated G

Application of the above rules to SEQ ID NOs: 14 and 15 results inrecovery (after removal of the linker sequence nnnn) of the originalsequences, i.e., SEQ ID NOs: 5 and 6. An alignment of reads a and b withthe forward strand of the original sequence is shown in FIG. 10B.

(SEQ ID NO: 14) a => 5′-AGATGTGGATGGGGTGGGTGGAGGTGGGTTGGGGC-3′(SEQ ID NO: 15) b => 5′-AGATGTGGACAGGGTGGGCAGAGGTGGGTTGGGGC-3′(SEQ ID NO: 5) r => 5′-AGATGTGGA^(m)CGGGGTGGG^(m)CGGAGGTGGGTTGGGGC-3′(r_a) (SEQ ID NO: 6) 3′-TCTACACCTG^(m)CCCCACCCG^(m)CCTCCACCCAACCCCG-5′(r_b)

Example 4 Comparison of the Accuracy of Simulated Single Read andMultiple Read Sequencing

The sequence of an assembled Escherichia coli genome, GenBank accessionNo. 000096, length 4639675 bp, was downloaded from GenBank. Randomlyselected fragments with lengths ranging from 500 bp to 2000 bp wereextracted from this sequence. These fragments were designated mastersequences.

Five subsequences were generated from the master sequences bycomputationally introducing deletion and misreading errors at definedrates, as shown in Table 7.

The five subsequences, containing errors, were subjected to a multiplesequence comparison analysis using the CLUSTALW algorithm (defaultsettings). The results of the CLUSTALW analysis were used as input forthe program “cons” of the EMBOSS package in order to obtain a consensussequence. The program “cons” is described in Rice et al., Trends Genet.16, 276-277 (2000), and Mullan et al., Brief Bioinform 3, 92-94 (2002).

The first subsequence and the consensus sequence were each compared tothe master sequence, and the frequencies of gaps and misreads weretabulated; see Table 7. The results demonstrated that forming aconsensus sequence using multiple reads reduced the frequency ofmisreads and gaps at each of the various error rates that was tested.For each set of deletion and misreading error rates, a single simulatedread and a consensus sequence determined from 5 simulated reads werealigned against the master sequence. The number and percentage ofmisread and gapped positions were determined as a fraction of thepositions in the alignment.

TABLE 7 Accuracy of consensus sequences determined from 5 simulatedreads compared to individual reads at varying error rates Rate of Lengthof Single vs. Consensus vs. Introduced Master Master Master Errors (nt)Misreads Gaps Misreads Gaps 5% Deletion 816 53/816 47/816  8/817 5/817 1% Misreading  (6.5%) (5.8%) (1.0%) (0.6%) 5% Deletion 1,565  90/156574/1565  9/1565 4/1565 2% Misreading  (5.8%) (4.7%) (1.0%) (0.3%) 1%Deletion 1,589 401/1602 41/1602 90/1593 5/1593 30% Misreading (25.0%)(2.6%) (5.6%) (0.3%) 1% Deletion 760 182/764  11/764  47/761  1/861  30%Misreading (23.8%) (1.4%) (6.2%) (0.1%)

Example 5 Simulation of Determination of Sequence Using a cPLM

A double stranded nucleic acid sample is provided as in Example 2. Theforward and reverse strands of the sample are locked together byligation of an insert that forms a hairpin to each end of the moleculeas shown in the cPLM construction step of FIG. 14 to form a circularpair-locked molecule. A single molecule sequencing by synthesis reactionis performed using a primer that binds to one of the inserts. Sequencedata is obtained that comprises at least one sequence of the forwardstrand of the sample and at least one sequence of the reverse strand ofthe sample. The sequence data is analyzed by comparing the sequences ofthe forward and reverse strands of the circular pair-locked molecule todetermine the sequence of the nucleic acid sample according to Table 8.

TABLE 8 cPLM sequence determination rules Acquired sequence Originalsequence Templated by Templated by Forward strand Reverse strand forwardstrand reverse strand (5′ => 3′) (3′ => 5′) A T A T T A T A C G C G G CG C

Note: in Table 8 and Tables 9-11 below, the acquired sequence templatedby the forward strand corresponds to the upper line of sequencing data(i.e., the sequence shown beneath the arrow labeled “Sequencing” andabove the arrow labeled “Sequence analysis”) in FIGS. 14-17,respectively. Similarly, the acquired sequence templated by the reversestrand corresponds to the lower line of sequencing data in FIGS. 14-17,respectively.

Example 6 Simulation of Detection of Methylation Using Conversion of Cto U by Bisulfite Treatment with a Circular Pair-Locked Molecule

The general scheme of this Example is shown in FIG. 15. A doublestranded nucleic acid sample comprising at least one 5-methylcytosine isprovided as in Example 2. A circular pair-locked molecule is formed asin Example 5. Bisulfite conversion is performed as in Example 2.Sequence data is obtained as in Example 5. The sequence data is analyzedby comparing the sequences of the forward and reverse strands of thecircular pair-locked molecule to determine the sequence of the nucleicacid sample and the position of the at least one 5-methylcytosineaccording to the rules in Table 9.

TABLE 9 cPLM/bisulfite treatment sequence determination rules Acquiredsequence Original sequence Templated by Templated by Forward strandReverse strand reverse strand forward strand (5′ => 3′) (3′ => 5′) A T AT T A T A C A C G A C G C C G G C methylated G C C methylated G

Example 7 Simulation of Detection of Methylation Using Conversion of mCto T by Photochemical Transition with a Circular Pair-Locked Molecule

The general scheme of this Example is shown in FIG. 16. A doublestranded nucleic acid sample comprising at least one 5-methylcytosine isprovided as in Example 3. A circular pair-locked molecule is formed asin Example 5. Photochemical transition is performed as in Example 3.Sequence data is obtained as in Example 5. The sequence data is analyzedby comparing the sequences of the forward and reverse strands of thecircular pair-locked molecule to determine the sequence of the nucleicacid sample and the position of the at least one 5-methylcytosineaccording to the rules in Table 10.

TABLE 10 cPLM/photochemical transition sequence determination rulesAcquired sequence Original sequence Tempiated by Templated by Forwardstrand Reverse strand reverse strand forward strand (5′ => 3′) (3′ =>5′) A T A T T A T A C G C G G C G C C A G C methylated A C C methylatedG

Example 8 Simulation of Detection of 5-Bromouracil Using a CircularPair-Locked Molecule

The general scheme of this Example is shown in FIG. 17. A doublestranded nucleic acid sample comprising at least one 5-bromouracil isprovided. A circular pair-locked molecule is formed as in Example 5.Sequence data is obtained as in Example 5. The sequence data is analyzedby comparing the sequences of the forward and reverse strands of thecircular pair-locked molecule to determine the sequence of the nucleicacid sample and the position of the at least one 5-bromouracil accordingto the rules in Table 11.

TABLE 11 cPLM/5-bromouracil sequence determination rules Acquiredsequence Original sequence Templated by Templated by Forward strandReverse strand reverse strand forward strand (5′ => 3′) (3′ => 5′) A T AT T A T A C G C G G C G C G T A 5-bromouracil T G 5-bromouracil A

The specification is most thoroughly understood in light of theteachings of the references cited within the specification. Theembodiments within the specification provide an illustration ofembodiments of the invention and should not be construed to limit thescope of the invention. The skilled artisan readily recognizes that manyother embodiments are encompassed by the invention. All publications andpatents cited in this disclosure are incorporated by reference in theirentirety. To the extent the material incorporated by referencecontradicts or is inconsistent with this specification, thespecification will supersede any such material. The citation of anyreferences herein is not an admission that such references are prior artto the present invention.

Unless otherwise indicated, all numbers expressing quantities ofingredients, reaction conditions, and so forth used in thespecification, including claims, are to be understood as being modifiedin all instances by the term “about.” Accordingly, unless otherwiseindicated to the contrary, the numerical parameters are approximationsand may vary depending upon the desired properties sought to be obtainedby the present invention. At the very least, and not as an attempt tolimit the application of the doctrine of equivalents to the scope of theclaims, each numerical parameter should be construed in light of thenumber of significant digits and ordinary rounding approaches. Therecitation of series of numbers with differing amounts of significantdigits in the specification is not to be construed as implying thatnumbers with fewer significant digits given have the same precision asnumbers with more significant digits given.

The use of the word “a” or “an” when used in conjunction with the term“comprising” in the claims and/or the specification may mean “one,” butit is also consistent with the meaning of “one or more,” “at least one,”and “one or more than one.” The use of the term “or” in the claims isused to mean “and/or” unless explicitly indicated to refer toalternatives only or the alternatives are mutually exclusive, althoughthe disclosure supports a definition that refers to only alternativesand “and/or.”

Unless otherwise indicated, the term “at least” preceding a series ofelements is to be understood to refer to every element in the series.Those skilled in the art will recognize, or be able to ascertain usingno more than routine experimentation, many equivalents to the specificembodiments of the invention described herein. Such equivalents areintended to be encompassed by the following claims.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although any methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of the present invention, the preferred methodsand materials are now described.

The publications discussed herein are provided solely for theirdisclosure prior to the filing date of the present application. Nothingherein is to be construed as an admission that the present invention isnot entitled to antedate such publication by virtue of prior invention.Further, the dates of publication provided may be different from theactual publication dates which may need to be independently confirmed.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1-36. (canceled)
 37. A system comprising a sequencing apparatus operablylinked to a computing apparatus comprising a processor, storage, bussystem, and at least one user interface element, the storage beingencoded with programming comprising an operating system, user interfacesoftware, and instructions that, when executed by the processor,optionally with user input, perform a method comprising: a. obtainingsequence data from a circular nucleic acid molecule comprising at leastone insert-sample unit comprising a nucleic acid insert and a nucleicacid sample, wherein: (i) the insert has a known sequence, (ii) thesequence data comprise sequence of at least two insert-sample units, and(iii) a nucleic acid molecule is produced that comprises at least twoinsert-sample units; b. calculating scores of the sequences of at leasttwo inserts of the sequence data of step (a) by comparing the sequencesto the known sequence of the insert; c. accepting or rejecting at leasttwo of the repeats of the sequence of the nucleic acid sample of thesequence data of step (a) according to the scores of one or both of thesequences of the inserts immediately upstream and downstream of therepeat of the sequence of the nucleic acid sample; d. compiling anaccepted sequence set comprising at least one repeat of the sequence ofthe nucleic acid sample accepted in step (c); and e. determining thesequence of the nucleic acid sample using the accepted sequence set,wherein an output of the system is used to produce at least one of (i) asequence of a nucleic acid sample or (ii) an indication that there is amodified base in at least one position in a nucleic acid sample.
 38. Astorage encoded with programming comprising an operating system, userinterface software, and instructions that, when executed by theprocessor on a system comprising a sequencing apparatus operably linkedto a computing apparatus comprising a processor, storage, bus system,and at least one user interface element, optionally with user input,perform a method comprising: a. obtaining sequence data from a circularnucleic acid molecule comprising at least one insert-sample unitcomprising a nucleic acid insert and a nucleic acid sample, wherein: (i)the insert has a known sequence, (ii) the sequence data comprisesequence of at least two insert-sample units, and (iii) a nucleic acidmolecule is produced that comprises at least two insert-sample units; b.calculating scores of the sequences of at least two inserts of thesequence data of step (a) by comparing the sequences to the knownsequence of the insert; c. accepting or rejecting at least two of therepeats of the sequence of the nucleic acid sample of the sequence dataof step (a) according to the scores of one or both of the sequences ofthe inserts immediately upstream and downstream of the repeat of thesequence of the nucleic acid sample; d. compiling an accepted sequenceset comprising at least one repeat of the sequence of the nucleic acidsample accepted in step (c); and e. determining the sequence of thenucleic acid sample using the accepted sequence set, wherein the methodresults in output used to produce at least one of (i) a sequence of anucleic acid sample or (ii) an indication that there is a modified basein at least one position in a nucleic acid sample. 39-68. (canceled)